I need help dealing with my brother not understanding that it is time for our mom to get some help at home! He bucks me on everything!

Who has POA for finances or health? Either of you?
If neither then one or the other will need to obtain Guardianship in order to make decisions for her. This includes her care. And paying for her care.
Mom's assets should be used in paying for a caregiver.
Are you and your brother actually taking turns moving into mom's house and living there full time for the weeks you are "on duty"? Do either of you work? Mom should not be left alone.
Contact your local Area Agency on Aging to determine what is available in your area and what services she might qualify for.
It might be better if mom were placed in Memory Care so that she is take care of full time in a facility that has the right set up and equipment to care for her.

Sometimes I wished that I was an only child. Debating with siblings is so stressful! Many of us have been through the same thing as you are. We had differing opinions and it is difficult to communicate with them when emotions are at their peak.

The conversation that you should be having at this point, is placing your mom in a facility. Call Council on Aging to do a needs assessment and go from there. Invite your brother to hear the results. He may be in denial about how much care that she is going to need. As time goes by it will become even worse.

Wishing you and your family all the best.

It would be helpful to know who has PoA and if it's springing or durable. Does she have a medical diagnosis by a doctor of cognitive/memory impairment? If not, maybe this would help your brother understand more. If both of you are PoA, then you are stuck working out what is the definition of "in her best interests" but is not onerous to her caregivers.

If I were in your shoes I'd have a calm (and even scripted) discussion with your brother about how you very much desire that your mom get the best care possible, but that you are no longer willing/able to do the "hands on" part since it is forcing you to put your immediate family as second priority, and this is not tenable since the intensity and amount of her care will only increase. Then I would offer some solutions that I researched, like in-home care and services (and the cost), vs. facility care (and the costs, having visited ones that'd be the best fit for her). I would take my own pictures of each facility and show brother that they are nice, well-managed places.

If affordability is a concern, you can assure brother that Medicaid is there to cover LTC and MC 100% when she needs it (and some states even cover some or all AL). You are under no moral or ethical obligation to provider all her care yourself, so you should be guilt-free in informing him that you will be managing in-home services for her that cover what you've been doing to this point. He can keep doing what he's doing. You don't have to. If he doesn't like that arrangement then he can attempt to cover both of your "shifts" but we all know how that will probably end up.

I'm hoping your brother isn't motivated by perceived inheritance, which often drives adult children to make some very poor caregiving decisions, for their LO and themselves. Which brings up the point that you should see an elder law attorney/estate planner/Medicaid planner so regarding your mom's financial oversight, since it is very easy for a PoA or well-meaning adult child to mismanage this part in the eyes of Medicaid and thus delay or disqualify her. Many states have a 5-year "look-back" on the application and get tripped up because they are unaware of this. And, if she's getting any sort of extra pension besides SS, she may never qualify but not have enough money to cover the significant cost of advanced care. I wish you much success in getting your brother on board.

If you haven’t already, click on the link under your post called
”activities for daily living”.
Print out the form provided and do the exercise of identifying where mom is now on each task. You might look at photos on your phone of past events a year ago, 6 months ago or even just 3 months ago and use them to trigger memories of how she was doing during those visits and how she is declining. Date the form for future reference. Ask your brother to do the same.
Realize that one fall, UTI or other life event can change everything. What looks now like a slow decline can move rapidly.
The fact that you are spending time with her for weeks means you already know what the issues are but do take a look at the other links. The more information you have that is factual and not emotional might help in your talks with brother.
You don’t mention if you have POA? If you do, I would hire help when you are there with mom to do the things you have identified. This gives you a chance to train them, to monitor, to see that mom is comfortable. Even if you just started with a housekeeper it would be a start.
Ask her doctor to order her home health to come out and access her abilities, check her home for safety etc to see if she qualifies as a homebound senior for a weekly visit, for setting up any meds and for a bath aide and for physical therapy. If she has traditional Medicare, this is a benefit of her policy. If her needs aren’t that advanced, at least you will know about the services. Take some action each time you visit. To me, personally, not everyone else’s opinion, but to me, life has to be managed. You can’t live someone else’s life. Not mothers or brothers. If he balks, it’s on him. If he wants to do things differently and he has POA then give him notice that you will come for visits but not for caregiving or whatever level of involvement you choose. Remember that we don’t all arrive at the same conclusion at the same time. Some of us need more time than others. In the final analysis some of us are more romantic than others, more sentimental but few of us can handle adult dirty diapers for our parents.
Read the book “Being Mortal: Medicine and What Matters in the End” by Atul Gawande.
I just noticed that your post is two months old. Give us some feedback if you are still with us.