Having gone through this with my own mother 4 years ago, let me give you advice you should follow:

Take care of yourself first.

If you put her and everyone and thing else first, you will burnout very quickly and still have the frustration and guilt and all that piled on.

Don't reschedule your new T appointment. Your mother can wait on leaving the hospital, or have an ambulance deliver her home if she is still able to make her own decisions.

Are you in the USA? If so, then you must have your mom sign a living trust, with you as Trustee. Otherwise, with just a will, things go through probate and the delay and expense is avoidable with a trust. You can go to SuzeOrman.com and download one for free. If you don't find it there, let me know and I can get you a copy fast. (In Florida you don't even have to legally file a Trust and it's legal..) you will need a notary for her signature.

Does your brother live at your mom's? Check with your mom's will lawyer (he should have Trust documents as well, but will charge you when you don't need to pay for them)... see if there is some way to give your brother notice now, before your mom passes...or if you can have your mom put something into the trust that removes him so you can sell the home?

I know this is a mess already, with guidance you will make it less of a mess.

GO SEE YOUR new Therapist! Good self care is very important right now, and you're needing support hon.

I'm concerned for you in this ... but care so PM me if you need more support to do what's best for YOU in the long run, okay?