My sister and brother gained POA over my father's finance and living trust. Can sister change address and make deposits when she's not POA for my mom?

It sounds like you have a large family. It’s good your mom can still make decisions as to who she wants to handle her affairs.
I would block the number of the person who is harrassing you if it is too upsetting.
I asked a police officer once if a neighbor cursing a relative was abuse. He asked if my relative answered back. I said no, why?
He said,
“If you answer back it’s an argument. If you don’t, its harassment on their part.” He was a police officer not a lawyer but that makes sense to me.
Don’t answer back, then you are in the clear. Come here to vent.
But do get your mom back to her attorney or at least the POA to take right action on outlaw sisters antics. Probably a letter from the lawyer would make an impression. Also no Facebook chit chat or other social media or gossiping with other relatives and friends. That’s just stirring the pot.
As long as the POAs are doing a good job, documenting all expenditures etc, then if Outlaw sister or her daughter took you to court, what could she prove? That you were doing a good job?! Mom is healthy and happy and well cared for should be the focus.
And how does the sister know she’s not in the will?
See what I mean? Someone talking about someone else’s business.
Zip it for peace in the family.

Yes a lawyer did the POA’s and will. My sister’s daughter is accusing us with the elder abuse in text message and stealing from my dad. Everything we have done has been put in my moms name. They are bitter cause my mom didn’t add them to her will and that decision was done with her and the attorney. The sister had taken an attorney when my dad was in ICU and appointed herself and another brother as executor/ Trustees on his living will. Since he’s deceased my mom became the sole beneficiary and sister was trying to say my mother is incompetent to make decisions. My mother was cleared by a doctor saying she can make decisions and appointment who she wants to handle her affairs. This is how it all started.

No. It is not legal if you and your brother are POA for finance and medical. Does your mom live alone?
Change the address again. Contact your mom’s pension distributor and give them a copy of the POA. Set the checks to be auto deposited in your mom’s account.
You may need to go back to your mom’s attorney and ask for help in getting sister under control.
Who is the text from?
If you are taking good care of your mom you should have nothing to worry about. Keep good records of all your mom’s finances. See that she is well taken care of.
I’m sorry for the death of your father.

Did a lawyer help with changing the POA to you? Did the lawyer notify the previous POA?

What is Mom's living arrangement?