My sister and husband are on mom's bank account. How do I find out what they're paying?

As Jeanne said, you need to find out if they have power of attorney. Is mom able to answer that question in her present state of mind? She would have been the one signing that power over to them.

It is for that reason I insisted on having joint POA with my brother. He lives in another country and really didn't care one way or another if it was joint as he has no responsibilities regarding mom's care. I want everything to be transparent and keep records down to toothpaste receipts. He also has access to the online account if he chooses to look.

I hope your mother is able to clearly tell you if she signed POA papers. I would asked to be added by her so you can have access to her statements. Jeanne's right. It's your mom's account. Ask to see her statement.

Do they have POA for mother's financial affairs? If not, and Mom is willing to make you her POA agent that would give your some authority.

If one of them has POA, then they are not required to show records to you. If you suspect that they are stealing her funds and have some concrete reasons for your suspicions then you could report the situation to Adult Protective Services.

And, of course, it is Mother's account and she can show you anything she wants to about it.

Unless they show you a bank statement, there really is no way for you to really know how the money is being spent. When you say they are on her bank account, do you mean as co-owners or as signatories. Either way, unless they want to disclose that information they don't have to.