What do you do if your aging, alcoholic father can no longer adequately care for your mother who has deficits from a stroke?

If you wish to help them when an opportunity arises, you would ideally need your parents (or your mom at the very least) to assign you as her PoA. What I did with my resistant MIL is have the paperwork for our state already printed out. I used Legalzoom.com and it's inexpensive and convenient. You don't need an attorney if you just need a basic PoA. Print out 1 copy for each person: your mom and however many PoAs she may assign (hopefully 1 but no more than 2). Everyone needs an original copy. You can print out one for durable PoA and review it with your mom to see what authority she wishes to allow you to have. Then you must take the paperwork and 2 witnesses to a notary (usually at your bank, a free service), have your photo IDs with you and sign all the copies in front of the notary. This is what I did for my mom and MIL. Then take her to her bank and do whatever her bank requires to get the PoA authorized (it is a slightly different process). Medically, even is you are her medical PoA you will need to have her assign you as her Medical Representative in order for her doctor to discuss her medical info with you without her present. This is part of the HIPAA law.

A crash and burn is inevitable for your father. With no PoA it is true that your only recourse is calling APS. This will set the wheels in motion for the county to pursue guardianship for one or both of them, if the county thinks they are no competent as vulnerable adults. The the guardian will make all their care, placement, financial decisions and perform management duties of their affairs going forward. If they require Medicaid, the house will have a lien on it, if they own it. The family will not be privy to any more information (you will be locked out of all their accounts. But they will receive care and be protected and you can still carry on your relationship with them wherever they live.

I think Alva is right; there isn't much you can do if your parents don't want help. If your mom wants your help, I guess you can move her in with you, but it sounds like she feels like she can manage at home where she's at now, with your dad, right? If so, you can't force the issue. I don't blame you for feeling nervous, though, I would too if I were in your shoes. It's so sad when someone goes down the addiction road and we all have to stand back, helpless to really 'do' anything about it. It's your DAD who has to want to stop drinking in order to facilitate a change. Or else something bad has to happen, like Alva said, in order for change to be forced upon them.

Until then, you can call APS for a wellness check to be done, but unless they're living in total filth and grave danger, APS will probably say everything is fine. Go over and check on mom as often as possible, I suppose that's all you can do. And tell her to call you if she needs anything, day or night.

Wishing you the best of luck with a nerve wracking situation.

As your Mother and Father are of sound mind there is little that you can do if they refuse your help. You can speak with your Mother, but it is unlikely she will separate from this man at this point, and it is more unlikely that your Dad will do what you wish. The poop will eventually hit the fan and arrangements will have to be made. Meanwhile hopefully you are POA in the case of someone who cannot act on his or her own behalf.
You really have no options. They are the ones with options. And they are not making use of them. As to making too much Social Security to get aid, that isn't really how it works. The nursing home or facility they are in will take the social security as partial payment and then medicaid will kick in. So placement is an option when it is needed.
If you feel your Mom is unsafe with your father it is likely time to open a case with APS to have an investigation and wellness check.