If taxes are being taken out of mom's retirement benefits, should I file on her behalf or should I claim her on my taxes?

This question would be best answered by an Accountant or CPA as there are a lot of variables in place.

I believe in order to claim your Mom as a "dependent" on your taxes, you would need to be paying 51% of all of her care, housing, food, clothing, etc.

You might also try looking at the IRS website under claiming a dependent. That should provide some guidance on when you can claim someone as a dependent.