Does my dad have the right to stay in a home belonging to his legal domestic partner in Washington state after she goes into memory care?

Yes, who has been assigned DPOA. Does SM have a Will stating that Dad can remain in the home until he either leaves or passes away and then it reverts back to her daughters? Anything in writing saying he can stay.

"daughters recently said that we should get in home care so my dad wouldn’t have to be displaced." So this means that if Mom goes into MC that Dad won't be able to stay. That the house would need to be sold for her care in the MC? Yes, you need a lawyer well versed in Medicaid rules. Him living there paying the bills may give him some rights.

Just affirming that each state's laws can be different so best not to crowdsource an answer to an important legal question. On another note, you dad may want to stay in the house and "age in place" but is it financially realistic for him? Or will it require his family to orbit around him in order for this to take place? Does he require help to mow, shovel, maintain, clean? Does he still drive and cook for himself? Your dad is the only one who should be paying to make it possible for him to stay put. It is amazing how much time and effort is required for other family members to help a single LO stay in their home. Please go into this with your eyes wide open, since the caregiving arrangement must work for both parties (the care receiver and the care giver). I wish them all the best during this challenging time.

Your dad needs to see a certified elder attorney well versed in Medicaid for their state.
In some states, spouses have the right to stay in the home until they die or want to leave, even if the owner wills it to someone else. There’s the comingling of assets issue for repairs etc. that can cloud ownership. I’m confused when you say he has paid rent. You refer to him as a “ legal domestic partner” and her as “step mom” so your post is confusing on the actual legal set up.
Unless someone has deep pockets, Medicaid is likely in SMs future and possibly your dads. It will be important to make sure the application is filled out properly to protect both their rights. Dad needs a certified elder attorney. Perhaps you could help him find out how to get SM help without jeopardizing his own situation.

I am also legally a domestic partner. In my own state I have many many rights afforded to a spouse. However, a home is owned by the person who is on the deed, and absent any stipulations by Trusts or legal instructions, things depend upon the rules in your state. Every state is different. Also, it should be known that the name on the deed of a property is the name that property belongs to. If there are other writings, say a trust that the property is in, designating rights of domestic partner to live in life estate that will be written out. If not, I can only suggest you see a lawyer now in your own area who specializes in elder care and take all papers, domestic partnership, deed, any wills/trusts/etc. you can find along with you. You definitely need to know your father's rights as Domestic Partner. Is your Dad the POA for his wife? If so, the daughters cannot dispose of this house; that would be up to your Dad as representative of his partner. Is he guardian of his domestic partner? If not, explore this with the attorney. He would likely win guardianship if he is competent and wishes to have it. Then no one could sell her home until her death, and only her legal executor or the executor appointed by the court at that time. This would leave your father living in the home at least until her death. Go now with your Dad to find out what his rights are as a Domestic Partner in the State of Wa.

I'd talk to a lawyer. In many states, living together for 7 years constitutes a legal marriage, with all benefits, etc.

Just my thoughts--best to see what the law is in WA.