I don't know what to do either. She keeps telling him to get out of her house and she is not ready to go to a nursing home and I don't want to do that either. She barely remembers I am her daughter so I have to worry about my dad now, how do we explain to her it is both of their house and that is her husband
I will cross my fingers tightly that the uti FF mentions as a possibility proves to be a factor and treating it will help settle your mother down. Unfortunately, though, if this behaviour is emerging as part of her dementia then it will be back sooner or later, uti or no uti; so start looking at your options now.
I do honestly understand that neither you or your father is happy to think of "locking her away." But if it's going to be necessary for both her and his safety then it's better to try to get ahead of the game and find her the right place, with the right support, while there is still an earthly chance of her being admitted as a functioning person with some ability to relate to the people around her.
Meanwhile, do not attempt to convince your mother that the "strange man" is her husband and lives in the house. You will only alienate and anger her further. Look up Teepa Snow for techniques; but broadly speaking you want to aim to reassure her that it's ok for the strange man to be there because... [insert reason that she can accept, such as that he's come to help maintain the house or whatever might apply in their case]; and divert her attention to a new subject. If she doesn't always fail to recognise him then you may find that after a while she accepts his presence again. He will need to figure out some routines that work for him, too.
There is a saying that "if you know one person with dementia, you know one person with dementia" - so other people's advice, however accurate and based on experience, is bound to be limited in terms of its practical helpfulness to you and your parents right now. But please be encouraged that you will find approaches that work for you and your father, and you will become the expert on your mother. I'm so sorry for what you're going through, please come back and update us.
If Mom has a UTI and it is cleared up, and she is still acting this way, then it sounds like dementia is now part of her life.
Learn all you can about Alzheimer's/Dementia https://www.agingcare.com/alzheimers-dementia
Rather than tell her Dad is her husband, can you say --first name, Jim for example - is here to help you . Isn't he nice to do that? Posit it as an ally - someone she can count on.
Also, the alzheimer's organization (which also covers other dementias) has a 24/7 helpline you can call. 1.800.272.3900. Can you and Dad join support groups for this disease? You can find them on the Alzheimer's site alzdotorg