Can I sue?

Power of attorney for your father is now impossible because he is deceased. You could file to administer his estate in probate court but if there...

Can the mother give up her rights to her mother if I have temporary full custody?

What is the "paper that says...."? If it is a delegation of parental authority, I do believe an order from a court of competent jurisdiction would...

They have the legal right. Your daughter is a minor being supported by someone other than yourself or your husband.

It is very possible he has committed bigamy. There are a couple of exceptions but that is up to the alleged bigamist to inject those facts.