How much time to give mum for deciding on living arrangements?

Thank you so much everyone. To clarify the financial bit: yes I live in the UK but not originally from here, I immigrated and built my life here. I brought mum over here, so added issues of social/cultural integration for my mum. She has done a lot in this respect, learnt the language, she has a few friends, has done courses and travelled. But she often says she is lonely and lacks communication. And re finances: she has her own place back in the country where we're from (rented out, it provides for the complement of pension). The state pension where we are from, buys a couple of weeks worth of food in the UK... hence why I shoulder maybe 80% of her financial needs.

Update though: I had the first initial talk bringing up the subject, today, while son is with his dad for a few days. Big shock and a bit of tears from mum, although less than usual of accusatory/complaining monologues about how she is my slave. OK, so the subject is in the open, she tearfully said she hopes I am not kicking her out right away and says she is willing to talk about what's not working. Made me sad / compassionate for her. We agreed to take 48h to time out and talk again more calmly. I still believe, despite the hard feelings, now that the subject is in the open, I need to press on and drive to the conclusion that we need to live separately. I agree with the posters that issues will only multiply down the line. She raises good points like, what if I fall sick with covid, who will care for my son, etc. Clearly I will need to re-think the child care and home keeping strategy. Her own place can be sold for the price of maybe 1/4 the price of a one bedroom apartment next to where I live. She does not want to go back to our home country. I think we could make it work with agreeing that I initially shoulder the rent and when she sells her apartment we maybe figure out buying a small place for her with my help / mortgage (would be on me). Further thoughts and ideas welcome. I will sleep on it before our next talk with mum. Thanks all so much for support.

This is probably going to be hard to undo. When my oldest child was a baby, I accepted a large amount of my mother's time in terms of child care. My husband was laid off (no fault of his own), but was back in school full time with homework in the evenings and significant commuting time each day. I was working 55-60 hours a week at a "salary" job, so I was only getting paid for 37 hours a week. It was chaos in terms of time and finances, but I had to carry the medical insurance and keep the household afloat. My mother had always been bossy, controlling, and even a liar at times if it got her what she wanted. In spite of that, she was still the logical person to help me and I was cautious about strangers. I was willing to go into debt to hire a part time nanny through an agency, but somehow changed my mind or got talked down from that. I did have several other fill-in babysitters, but mom was primary. Over time, she got more and more bossy/controlling and she seemed to honestly believe she had final say over educational and other major parenting decisions. She scared me at times - it was almost like she was revisiting her own parenting years and did she realize that? My child got older, hubby went back to work, I switched to part time work. We had to distance ourselves to some degree and give mom a chance to be present for other things and people. For her own health as well as to allow my family to function in its new form. To observers, it probably looked like I selfishly pulled back once I didn't need as much help with my child anymore, so I'd mention that as a red flag because you may be judged by others who really don't know the situation. Your mom seems to have a lot of emotional investment into YOUR life (I know mine did) and that will also make it very difficult to set boundaries and keep them. One other thing is that if you can't provide care to her as she ages, please make that known. I would hate to think she was assuming she could stay indefinitely. We had a situation personally where elder care was not addressed for a particular person and it was assumed that free in-home care would be provided to this person by family and friends. That's a HUGE assumption on elder's part, but it does happen and family/friends get left holding the bag or end up being the bad guy when they indicate "at the last minute" that they can't provide care.

For nine years you have supported your mother, starting from when she was 55 years old? You abdicated your responsibility to raise your child and allowed her to do so though you did not feel she was good at parenting? She has basically been in charge of raising your child while you worked, and for a decade? And her mode of raising children has left you with a bitter pre-teen son who is entering the most difficult years of his life?
You say your mother "retired". Had she no pension? She just was penniless all her working life and then just quit so you could work and support her? You knew she was raising your child in a way you did not like, yet you agreed to this for a decade. Now Mom is of Social Security age. I hope she is collecting it and saving every cent of it, because it is time to move out now.
This has been a decade in the making. It will certainly take 6 months to cure. But it is time now to sit Mom and Son down TOGETHER and to apologize for allowing this to go this far, and say that you take full responsibility for bad choices made during a time when you felt helpless, and for allowing them to go on for a decade, but that you WILL NOT allow it to go any farther. That you will attempt to assist Mom in finding a small studio nearby or even a room in situation with another like minded person, but that she will have now to leave your home. Tell your mother that the subject is not open to argument.
If it comes to who did this wrong then what does it MATTER at this point? You BOTH did, or NEITHER of you did, or hey, how about THIS???? Admit it is all your fault and you did it wrong, but that changes now. Tell your mother that you are allowing for a six month period in which she should save every penny of her retirement check (if there is one) and every penny of her social security, and she should immediately begin to look for a place to live.
This will leave you and your son with much healing to do, because for what has happened to him being raised by the Mom you describe, that is ALL your fault. Time to own it and move on. I would seek help so that you do not over correct, and set loose a lad who has no idea where to go or what to do with all the change. In this day and age of addiction available at every street corner this could not only be life changing but it could be fatal.
Fault can be leveled wherever anyone wants to place it. Fault is no longer the question. Now the question is how to change it. Plenty of guilt to go round if anyone choose to sink into that silly word. This is about mistakes, grief, and the courage to change. Guilt just doesn't figure in it, to my mind.

I am assuming here because you use the word MUM you do not live in the US but maybe the UK? If so, in the US after maybe 25 years our teachers can retire with a very nice pension. We also have Social Security and depending on the State teachers have paid into it. Then at 65 Medicare kicks in which pays 80 % of Medical. So a Principle, in my State, would get a nice pension and SS with it. Meaning, they have their own money. Your Mom has nothing? No pension thru the government?

What kind of help can a person like ur Mom get if u do live out of the US?

This is going to be so hard. Not sure if you can approach it as you never felt her living with u was going to be permanent? And now son is old enough to be left alone and seems like they r butting heads, maybe its time for Mom to find a place of her own. Get her own interests? Reason would be that son will be going off to College and you will be free to find your own interests. Not wanting to be Moms entertainment.

This is a good time to teach your son respect even though he maybe right. Tell him not to argue with her. If he has a problem, come to you. You may want to tell Mom that you appreciate everything she has done for you in helping to raise your son but...he is at an age now where he needs to answer just to one person, you. This may curb the arguments he has with grandma. If Mom has a problem with him, she comes to you. There should only be one boss at his age. I had no problem with my Mom because our parenting styles were the same. But my MIL, thats another story.

Why does she drive the decision? Isn't she in your home? Your immediate family (you, your kids) take priority over her. And, it is healthy for her to have her own life outside of yours. She won't want to do it, she won't like it, but this shouldn't mean she gets to stay. . You're not rejecting her and it doesn't mean you don't love her. You don't owe her any explanation or justification. She can still live close to you and you'd probably have a better relationship with her. If she stays, and declines in your home you are on a track to burn out.

My mom moved up from FL to MN where I live to help me with our kids while we worked and managed our business. My mom was a nurse/facility administrator and is also opinionated and headstrong. She lives next door to us but she's lost the sense of boundaries and as much as her help has blessed us enormously, it's created its own challenges as well. I vote for you to reclaim your life while it's still "easy"...the more decline your mom experiences while in your home, the harder it will ever be to bring about. This way, she is in full control of where she lives (not IF she moves out) and her own social life. I wish you much success in moving forward!