Mom has demensia, owns 2 homes, sold secondary home to pay for care,what do you recommend we do with $$ for the second to avoid taxes or probate?

You can place the proceeds into a special account and use those to pay for care.  If you want to avoid probate, you can always make that a joint account with another person but that money will still be considered mom's asset if mom needs to apply for Medicaid.  However, you have to be careful because if you are taking these actions as a Power of Attorney, everything you do must be in mom's best interests, not for your interest in avoiding probate or taxes.