How do I find a skilled dementia at home caretaker for my dad?

What services would your mother have the caretaker provide? From your description he sounds like he is functioning at a high level. Does he require prompting to carry out those self care activities? Does he require constant supervision? Is your mother unable to leave him alone while she is out of the house? Does she need a break from the house hold chores that need to be done day to day? I realize this is a lot of questions but his level of function and needing help 12 hours a day aren't matching up in my mind.

The agencies, like Home Instead, can provide you with someone, and it can be good to have them to turn to in case there are problems. The agencies will be more expensive than someone you hire privately, but you won't have to worry about paying their SS and withholding taxes.

I'm not sure how to find "independent" HHA's, but you can ask the doctor, and the local Area Council on Aging. Naturally, you will want to check references for anyone you hire, including a CORI check - criminal record. These people are not going to be PhD's, but some are very intelligent, have common sense and lots of experience. The right person will be a blessing to you all.