Op, I dont easy to over step. But I think you obsession with fairness is (potentially) part of your grieving for your mum and feelings a our your dad being in a home.
My mum died recently and everything does feel unfair. Really unfair.
However, on 95% of these threads where dils are complaining their pil are not fair, it always transpires they live further away than the sil, they perceive as being treated better.
Its a huge factor. Your sil and your husband likey have very different relationships with their parents. Most of which you won't be privy to.
Dbro and my sil went through a phase of saying I was treated better than they were. After we all talked it out their perceived slights were just that. Perceived. They now understood that I was closer to mum and dad and they spent more time with my kids because I made more of an effort.
I would visit them, to see them, not just when dropping the kids off for babysitting. I would take mum for appointments if dad was working. I would have them over for dinner. I would take them out, to take them out. Sil made it clear that her family was the primary family. And that was fine. But dbro made very little effort to actually care about them.
When mum died, just because Christmas, my brother is became full of regret about not fostering that relationship and is trying to make it up with dad. Dbro is a sahp so definitely had more time than me, but decides to priortise other things. They moved closer to sils mum which meant they didn't see my mum and dad ubl3ss they needed something.
And that's not actually wrong. But relationships are reciprocal. My Mum and Dad were a primary relationship for me. But not for dbro and sil. And again, it's not wrong. Also because they lived further away, their view of the situation wasnt clear.
Again though, I am not close with my mil. Because dp isn't. She is very close with her youngest dd. Again because of dd fostering the relationship. I do make an effort with mil and will visit just to visit, but not like I do with own parents. I will visit without dp. But I don't put as much effort in as I do with my own parents, so don't get the same out.
Just a different point of view for you to think about.