Father in law is driving me mad. Advice?

Sorry for not answering back for awhile. Personal life got a bit hectic. I made a mistake when I made my profile, I'm taking care of grandma, not grandpa. She's 80. FIL and MIL in their 50's. I don't live with them even though I spend most of my time there. FIL has not changed, I've come to accept that he is a narcissist. I've put down the options mil has. I told her to put her in a home, find a new caregiver, or give me some respite care. Neither has happened. She says she's looking into homes but I've not heard much on that front and FIL doesn't trust a stranger in the house which means no new caregiver or my respite. I've come to accept that I will just have to be patient and wait for them to figure out something new in the situation. Yes, it's really frustrating that I can't change all that much here and I can't just leave but at least grandma can live at home. I suppose that's a blessing I shouldn't overlook. Thank you for all your advice, I appreciate it so much.

First ages would help.
Second do you live with them or they with you.
Third where is your husband in all of this.

My daughter says...turn it back on them. Ask dear FIL if he would like to take care of grandma because you would gladly hand her over. (U may want to mention everything u do for her) Call his bluff. If he says no thats your job, then tell him if that is so then keep his opinions to himself. Your the Caregiver so things are done your way. Do not take anything from men like this. Stand up for yourself. If he starts hollering walk away.

I also would do nothing for this man. He can get himself something to eat, wash his clothes and clean up for himself. You have enough with grandpa. And DH needs to step up to the plate telling his Dad the same thing. "Wife will step out of the way and let you take over."

So is GM the mother of FIL? Does your husband help with this situation?
Perhaps you could contact your Area Agency on Aging and see if a case manager could come to your home and evaluate the situation. They could do a needs assessment and see what services might be available for your family. It certainly sounds like you could use some help.
It’s possible they could help FIL better understand GM’s condition.
Here is a link to their website. Look it over and give them a call.
https://www.lmtaaa.org/

This is an overview of what you can look for on the site.

https://www.agingcare.com/local/lewis-mason-thurston-area-agency-on-aging-olympia-area-agency-on-aging-wa

Your profile says that your caring for your grandfather. So your caring for your grandfather, and your husbands grandma? You've got your hands full for sure if that is the case. Do either of them live with you?
How does your father-in-law fit in this picture? Does he live with you, or just visits occasionally? I know you say that he "for sure doesn't have dementia," but if he's making things up regarding the care of his mom, it makes me wonder if perhaps he doesn't have some mental decline. I don't know. We're only hearing your side of the story, and as you know there are always multiple sides.
If grandmas care is getting to be too much for you and your father-in-law thinks he can do better, let him. You are not obligated to continue to care for her. If you're having to now wonder if she is going to wander away from home, it may be time for her family to be looking into placing her in the appropriate facility.

Do you live with both these people? The FIL and the grandmother? Because if not, I would cut the father-in-law no slack. Simply stop communicating with him. If you do live with BOTH of them, I don't see how that is going to work long term. It sure wouldn't work for me.