How do I deal with my father's delusions that my mother (who has passed) has run off with another man?

If he gets angry when you agree with him, don't agree with him. Don't try to reason with him and don't try to explain that your mother has been deceased for years.

When he starts up about yoru mother cheating on him and living with another man, tell him that is not true and you refuse to discuss it further. Never go along with a dangerous delusion like that. Then you totally ignore that subject. Refuse to pay any attention to that topic.
If you cannot divert him onto something else and is starting up about getting divorced and talking ill of your late mother tell him very calmly that you don't care what he does about that because it's none of your business. This way you're not agreeing or disagreeing with him. Do not discuss it and do not try to reason with him because that's impossible. Totally ignore that topic.

Never go along with a dangerous delusion. You say your father is getting paperwork together for a divorce so I'm assuming he's not in a memory care facility. He probably should be.

Don’t let yourself become part of his distorted thinking.

There’s no point in attempting to reason with him, so stop trying.

See if he’ll accept “I don’t know how to reach her by phone, but I’ll see if I can find out for you”.

Don’t agree with his angry reactions. Don’t take hi, to her grave. Don’t try “making him understand” anything. His brain is failing, and his ability to understand is diminishing as his brain fails.

Don’t encourage his work on his divorce, if it allow him peace, even temporarily.

The length or happiness of his marriage have no meaning to him now. Those things are part of your happy memories. His illness has stolen them from him.

It sounds from what you’ve described that you may need to consider looking for residential care (he may NOT need a nursing home, and there are many levels of care that may be VERY GOOD for him) just in case his needs exceed your very kind desire to provide for him in your home.

You suffered some terrible losses. Are you taking really good care of yourself? Please be sure that you do.

Poor guy. How heartbreaking for both of you.

My mother had an imaginary husband after forgetting my dad entirely. She'd get upset when the invisible guy wasn't around, so I'd give him some of my dad's attributes. I'd say, "He left really early for work this morning before you were up," "He'll be home after you go to bed tonight" or "Don't you remember him kicking you in bed last night?"

That usually calmed her down.

Can you think of any of your mom's attributes to apply? She's at the grocery store/getting her hair done/visiting her friend/relative?

Sometimes a plausible answer rather than even the truth of her death is enough to allow you to redirect them to another subject. Even walking out of the room for a minute or two, then returning as though it's a new day can help them reset.

I know that you don’t want to place him in a facility. You state that you bought his home and decided to allow him to remain in the home.

You also say in your profile that you lost your mom and your daughter. I’m so sorry for your losses.

You have returned to work. Your husband works too. Who is with your dad when you are working? It doesn’t sound like he should be left alone.

Please consider placing him in a facility where he can be cared for by a staff.

Have you discussed this situation with his doctor? Maybe meds could help with his anxiety over his delusional thoughts of your mom being with another man.

Best wishes to you and your family.

The key word here is " dementia" which sadly and tragically manifest in these behaviors that you are describing; they ( dementia) pts are unable to comprehend conversation ( trying to explain and correct is futile) and unable to retain ( short term memory loss) , hence they continue to repeat the same questions over and over, regardless of how many times they are corrected. Who knows why he is living her death as a divorce or her betrayal? Perhaps there were relationship issues long ago or insecurities on his part all thru the marriage ( that no one knew about) that are possibly contributing to his " reality" now; or maybe it's his way of denial if her actual death.
If you have him under the care of a Geriatric Specialist, this will be your best resource most likely on how to cope with and address your father. The reality is that your father's reality is just that, real, to him ! Trying to correct him is futile and anxiety provoking and exhausting for You and him. As long as he is safe and not harming himself nor others it is usually considered best to let the dementia pt be in the space ( mentally) that they are. This is awful to listen to, so redirection may be tried but may not help.
Protect yourself by getting counseling support, practice good self care, ( exercise, good nutrition, see your PCP etc) perhaps join a dementia support group for family/ caregivers, and be sure that you are getting respite care for him so that your physical, emotional, spiritual health can be addressed and nurtured. If he is in your home or you are in his home, it may be past time for you ( POA) to confer with his physician, and or Elder Care Attorney to get options and facility placement referrals for placement into a " memory care" unit.
Who is with him 24/7 now?
If you get ill or unable to care for him, who will care for him 24/7?
Are POA other legal paperwork in place so that you can make decisions on his behalf?

I like to just meet my mom where she is and help her work her way back to reality when this sort of thing happens. Typically it’s just after waking up so I figure she has been dreaming and is still in that dream, though she always seems to recognize me. Anyway without agreeing or disagreeing my answer to your dad would be “what would you like me to tell her”? Then depending on his answer maybe “where would I call her”? Or on from wherever his answers lead you. I know with my mom she ends up either recognizing the person has passed, asking me if they have or if she is in her house, whatever the dream was, all on her own and it’s much less stressful for both of us than it was when I tried to correct her or tell her she was wrong. I will warn you though this can be really hard on you and approaching it like an opportunity to gather information about the bad dreams that seem very real to your dad so that you can learn how to better understand his fears and help help him will make it easier. Not easy and probably still sad but easier. Best wishes through your journey.

My mother (96) believes that her mother is alive. Every morning without fail she will ask me "have you talked to Mama yet today?" And my answer is always "no not today". Then she lets is go.

When I have tried to convince her that her mother is dead is only upsets her and she flat-out refuses to believe it. Sometimes I tell her that her mother is with Jesus and that doesn't upset her - she will sometimes reply "I know".

If I were you, I would try tell my father that his wife was always faithful to him and has not run off with another man. Try to figure out what to say that will make sense in his mind of why she isn't there - maybe she is on a little solo vacation. Or maybe she is visiting family for a month.

This will most likely be on loop from now own no matter what you say, so you'll have a chance to try out different responses and see what works.

Please contact his physician with this issue. He is having delusions about your mom still being alive, as well as delusions about infidelity. The Alzheimer’s Association’s website (they cover all types in d dementia, with Alzheimers only being one of them) is a great resource as well. In addition to contacting his PCP, contact your local Alzheimer’s Association (alz.org) for support. I hope this helps both you and your father.

Fascinating. Ask him questions. "Really? She did? Has she ever done that before? Do you know the guy? Where did she meet him?"

You might learn a thing or two about their life you didn't know. 🤷‍♀️

See if you can get a name out of him. Look the guy up, if there's a real one. Ask him why she left. Did they have a fight? Should you try to find them? Does he have a message for her?

See what answers you can get.

He lives in a different reality, keep reminding him that she has passed away could make him re-experience the pain of loosing her each time. Acknowledge his feelings with something like 'I know you feel this way; however, Mom just went to the grocery store to....'. Let him know that she isn't around at the moment but will soon return.

Was your Mom a church goer? If so, tell him that she is at church working with so-and-so (someone that your Dad still remembers in a positive way). This should calm him down. The main thing is to acknowledge his feelings and avoid having him re-live any painful experiences. Since he has dementia, he will bring this up again, and you will repeat the same story.

Hope this helps.