As POA and caregiver, can I use my mother's money to widen my bathroom and install a new shower?

Legally yes, your POA probably gives you the right to spend your mom’s money on whatever she needs. Read it carefully.
However if she has the possibility of needing Medicaid in her future, you could run into problems.
Does your mom pay you to live in your house? If not, a care contract with her paying room and board might be a better way to go. Then you can modify your home at your own expense and no confusion on her owning any portion of your home to sort through.

If she won’t be using that bathroom then you can’t use her money.

I don't think so if Medicaid will be in her future with the next 5 years. Medicaid will look at it as a gift even though its for Mom. They figure you will profit from the remodel when you sell.