How do I handle the disapproving looks or questions like "why are you doing that now?" or "you're not even watching"?

If you're the age that your sig implies, i knew a lot of guys like that--single guys "helping out at home" in order to get free rent. These guys had no chance of having respect let alone a relationship and eventually that seeped through with each one of them. Their social skills are as a whole severely stunted--one showed up on my porch looking for SO and I said that WE were busy. The guy was like, what, his truck is here. They were so subsumed by mommy ethics that they actually persuaded themselves they were 12 or 8 or whatever.

Don't let that happen to you.

If the ONLY reason you moved in with her is to help with shopping and household chores then MOVE OUT. You can shop and help her with chores on the weekend or one or two other days of the week.
If however you moved in because she is starting to have problems with other things then it might be time to discuss Assisted Living.
Or if you moved in because it will make things easier for you (not paying a rent or mortgage or other household expenses) I suggest that you save as much as you can as fast as you can and move out.
Far to often caregivers get burnt out and this is even if the person they are caring for is grateful, and happy. Burnout happens faster if you are dealing with someone that is negative.
A few questions for you...
Did mom ask you to move in?
Has mom always been negative?
If mom did not ask you to move in is it possible that she is negative because you are in "her" space? If she has lived alone for a while it is difficult adjusting to a "housemate"
I know you are trying to help but is it help she asked for and needs?

Terij
Your post reminded me of a time during my moms last year. I would visit her weekly. I lived three hours away. I brought her food for her strict diet made to her specifications. I cleaned her home, did whatever needed doing. Each time I came in, I was already tired from the drive and the stress. It seemed to me that she was critical. I told her that when I came the next week, I would like her to say at least one positive thing before she started complaining. I had no expectation that would happen. The next week I was busy in the kitchen, trying to refrigerate the food I’d brought in as soon as possible. She walked in and said “It’s good to see you (long pause) I guess”. I burst out laughing and gave her a hug, I could tell she had thought about it and that was the best she could do. I accepted it.
It is difficult to be around a negative person. But like any job and let’s face it, it’s a job, you will have to deal with personalities and that can be taxing.
Set a routine, Decide what you will do and get it done. Then go for a walk. Release the negative energy.
Meditation is amazing at dealing with tough times. Even if it’s just five minutes, done regularly, it can change your life. A friend of mine has a sister who was diagnosed with “learned helplessness”. My friend pays her sisters mortgage. In exchange she requires her to go to her therapist weekly, walk each day, send her a text with two things she is grateful for daily. In the beginning she phoned it in. She lives in a beautiful retirement community in Orange County and she would do her walk in her condo! After awhile she started walking outside. Now she walks two miles a day. It’s made a huge difference in her life.
Small, steady steps will make a difference.
Consider that part of your job is to bring a little sunshine. You may have to borrow it at first or fake it till you make it. But try an experiment and see If your good example can soften your mom. You will have to fill up in some way in order to not absorb the negativity. Make sure you choose something that makes you happy. Exercise, writing, creative efforts, reading, singing, painting, making a perfect pie crust, giving yourself and mom a manicure, pedicure. Try to make her laugh and be sure to touch her everyday, hand her a Cup of tea, bring her a wrap. Give her a taste of what you are cooking. Woo her a bit. It sounds a bit corny but you won’t get this time back, I can tell you have thought of that. as the saying goes “bloom where you are planted”.
Small kindnesses. Difficult I know when you aren’t liking each other very much but see what’s at hand that will allow you to feel better about yourself and her. If you decide to do an experiment, let us know how it goes. We do want to support you.

Yes, living with a negative person can change your world.
Is your mother mental capable, not suffering from dementia? It is important then that you and she have an honest talk. Those have to happen with ANY two people living together, partners, spouses, parent and kids, whatever. GENTLE honesty is the key. "I feel", not "You did" statements.
Is this negativity of your Mom's something new in her personality? If so, ask her about that (this may be difficult for her as it is for you); or is this the norm for her? If this is her norm, ummmm, you just moved in with it. It would be unlikely to change now if this is her basic personality.
You may need some boundaries in the house. Some separation. It isn't necessary that you be together at all times. I have a much loved partner for 35 years now, and we are seldom in the same room doing the same thing. I garden while he putters in workshop. He watches CNN while I read. We do our computer in separate rooms at different times. Our hobbies are not the same. We get together over a favorite Radio or TV program and a walk, a game board. Because I love to eat my bigger meal at 3 pm and he at 6 pm, we seldom even eat together. Or eat the same things.
There is a way. This move, I assume is new for you.
And if there is NOT a way, and either of you is unhappy in the living situation, it is time to consider other options.
Meet with your Mom weekly or monthly and discuss "How is this working for us". If it works for both of you, good. If not, time to consider the options.

Terij, the reason why it matters whose idea it was for you to move in with your mother is that we need to understand where the disapproving looks and critical questioning come from. And to do that, it would be helpful to understand more about what your situation is and how you and your mother might feel about it.

This is not a criticism of you, it's a question about how things are. For example:

it could be that your mother has become, over the years, a negative person with a short temper who seems to be antagonistic towards you even though she asked you to come and be her main caregiver

or

it could be that you offered to move in to help your mother, and she agreed despite her private reservations and is now regretting it, and is demonstrating that by being generally grumpy.

When you say "I moved in with my 81 year old mother to help her with grocery shopping and chores" it sounds as though you mean the grocery shopping and chores explain why you would have made the major decision to leave wherever you were living, a considerable sacrifice for your mother's benefit. But the grocery shopping and chores DON'T explain it, and we need the rest of the picture to suggest ideas that might help make things more comfortable.

Sounds like you're getting a bit defensive with your responses to some of the kind folks trying to help you here. Sometimes in order to be able to offer a helpful response, we need to understand the whole picture. You may be more like your mom than you are willing to admit, and that's ok. It's never too late to change.

Perhaps start a grateful journal, where in it every day you write at least 5 things that you are grateful for. That way it helps you to remember that even though the day may have been a tough one, you still had some positive things to be thankful for. You'd be amazed how over time that will change your perspective on things, and keep you more positive. Wishing you the best.

More often than not, a reaction of "That's not what I asked!" is indicative a nerve has been struck.

Moving in with a parent to keep them company and run errands is much different than moving in to be a 24/7 caretaker. There's more to this story, and you of course are under no obligation to explain.

The "I'm reaching out to find support so that I can remember to stay grateful and happy" is troubling. It sounds like you WANT to be happy. You WANT to be a good daughter. But as much as you want all that, you know deep down that you aren't happy. And that doesn't make you a bad child or bad person!

I'm all for gratitude and positive thinking. Unfortunately, these actions don't help you out of your predicament. It just never works when you try to convince yourself you're happy, when you aren't. You're trying to drown out that inner voice telling you this arrangement isn't working.

It's also possible Mom has been negative her whole life, and you'd hoped she had mellowed some in her old age. Or that this arrangement would be a chance to patch up prior rifts and arguments, trying to make the mom/daughter relationship you'd always hoped to have. That it will all be worth it when she eventually passes, because you'll have had a loving relationship. A clear conscience, if you will.

There is nothing wrong or bad when we admit to ourselves that we've made a mistake!

I think it's relevant.

If my adult kid (still a kid to me 😉) moved in to MY home when I thought I was ok on my own I expect I would be pricklier than a cactus. I would say it's my house so it's my rules here.

Was setting up a cleaning service & grocery deliveries an option?

NA

Ummm.

It isn't obvious to me why grocery shopping and household chores would make it necessary for you to move in with your mother. Whose idea was it for you to move in, yours or hers?