I'm taking care of my mom (87) who lives with me full-time. I can't work because taking care of mom is a full-time job. Advice?

Take a breath.
首先我觉得你可能需要的是一个老care attorney. I also have some issues, but not nearly as much as you are going through. This is tough.. Wow. I don't have answers, but I pray someone with compassion and knowledge will help you through this. Let us know what happens. Get wise, stay strong.

Drop mom off on sissy's stoop with her bags. This has nothing to do with love but with being taken advantage of and winding up homeless and destitute, God forbid.

You can't make sissy give you access to mom's funds, but you can make her take HER turn caring for her and/or using mom's funds to hire in home help to do it for her. Because you need a job yesterday. One with health insurance benefits and a salary to help you pay the bills and avoid foreclosure.

Either that or sissy can pay you a salary that's enough to cover health insurance that you get a quote for before you have this conversation with her. It's going to cost her A LOT between the two.

What rent is mom paying?

So, is caring for mom a job?

Are you paid an hourly page, taxes, FICA and Medicare taken out?

If this is not the case, then something is wrong and you need to leave and get a job elsewhere

Inform the POA, give 14 days notice and leave.

So you are a slave. I hate to say it, but you created your situation because you let sissy do this. Now you need to make a plan.
You need to leave this situation.. Couple of options:
Bring her to your sister then say goodbye. Or tell her you are going job hunting and it is her turn to care for her. Sissy holds all the money so she needs to pay for mom's care.
Call APS and give your story about both of you being abandoned.
Contact a lawyer.