Does anyone have a referral for an attorney after being falsely accused as a caretaker? Has anyone taken this action?

I think you are wise to bow out.  You were properly investigated and exonerated - however, if someone like sisters or mom's ex-husband would go so far as to accuse you, this is malicious behavior and you would be wise not to play in that sandbox. Life is too short. And assisted living might turn out to be for the best as your mom declines with age.
And the advice to avoid lawsuit/lawyers is wise. Basically it would cost YOU too much.

Same happened to me twisted sissies called APS and claimed financial exploitation. One of those TS's was POA and KNEW nothing of the sort was occurring. They did not believe that mom was as sick as she was, denial is easier for the narcissist. We went to court, I was not going to leave, I was afraid that would make me appear guilty. Court found in my favor, ordered private guardian and conservator that were charged with auditing mom's accounts and the care I was providing. Everything reported as excellent care and bookkeeping, no exploitation or any other sort of abuse. Twisteds did not believe the reports. Then court ordered I be paid for caring I provided.

I paid my own attorney fees and once I was paid then I quit. Not because of mom, but just plain sick and tired of twisteds and their treatment of me to say nothing of the accusations. I did talk to an attorney about slander and libel. Those cases are very difficult to win, cost a lot to represent, and only occur in large companies that have deep pockets. Look at Budweiser and Coors current libel suit.

Just not worth the stress, effort, time and cost. Sometimes better to be grateful you are leaving with your health intact and peace of mind.

Speaking both as a lawyer and as a client of a lawyer during seven years of a fraudulent claim against us for damages, stay away from the law if you can. Once you get into it, it’s hard to calm down and find any other option – all those lawyers’ bills to pay for nothing achieved. And for a slander action, you need to prove damages. There aren’t any damages if everyone you know still thinks that you are a saint! You would be better off walking away and mending your own heart. It’s hard, but at least stop for a while before you make things worse. A one-off 'frightener' letter from a lawyer may be worth the money, but a full legal case will keep the hurt fresh for years.

Has APS spoken to you yet? Have they spoken to Mom or her ex? You maybe getting a little ahead of yourself. I would first allow them to do their investigation. The claims might be unfounded. If they find there is a problem, they will have to find a way to solve the problem with you out of the picture. Not sure if you can find out who filed the accusations. Lets say you are found in the right. You can voice that you strongly believe its who you think brought the accusations and that you will no longer do for them so APS will have to find services for them because you are walking away. They may not be able to tell you who but they can tell you who not.

If claims are unfounded you can hire a lawyer to bring charges against the person who filed the claim. Definitely if APS says your in the wrong, a lawyer should be able to get the info who put the claim in and have the ruling changed. But it will probably cost u.