Any advice on grandchild/granny relationship problem

I don't know what to do about this and my husband is less than no help. I asked 'mum friends' and their advice was basically '[expletive] your mother in law' and that advice is equally useless. Any hope of some more reasonable advice?

Sooo I have young primary aged children. My BIL has a partner who has a child of the same age. They have lived together as a family for some years now. My BIL is not the bio or legal father of his daughter, but she calls him dad and he takes a fatherly role to her. So far, so good.

The problem is, she has some behavioural issues (not a criticism, her parents recognise this and parent actively to deal with them) and whenever my kids are with her, there is invariably some incident of cruelty and violence towards my two youngest in particular.

I have begun to deal with this by not advocating for them to get together too often. My BIL and I have spoken about this in a low key tactful way - we don't think it's fair to put the kids together and have there be unhappy incidents each time. We will get to the stage where they refuse to be together at all and honestly my kids are vocal with me about preferring not to see her. They really worked hard at that relationship for a few years but there has just been continual water incoming under the bridge and it's like self-reinforcing now.

So sad as that is, we have that issue sorted in terms of we work around it as best as possible. Sometimes my MIL not unreasonably insists on having all her family together and I have given my kids some workarounds (bring books, video games etc on the visit, when she starts up just walk away from her and come sit with me, we have a codeword for 'something's happened and we really need to leave') to try and make that work. So we manage with that.

The metaphorical turd in the punch bowl is that my MIL demonstrates through gifts, actions, and especially through her conversation a strong preference for my BIL's daughter. And my kids are quick and have caught onto this, and they are really starting to not like it.

Examples: only her art/crafts are displayed in Granny's house, she is given more food/treats etc when they are together, she is given more presents, she is allowed to behave differently from them (NB: she does display behavioural issues but is not diagnosed with anything and will not be diagnosed, if she did have a neurodivergence issue I would fully expect the expectations of her to be different but that's not the case here). They already have a slightly iffy relationship because granny is very critical of everyone around her and sometimes they catch that too. I do step in around that. I don't care if I catch strays but I will not have them subjected to the kind of random hurtful nonsense she can fling.

They are always polite and well behaved when they see her. I know, mum on the defensive and all that, but my husband can also be very critical and he is clear they do nothing in behaviour or conversation for her to take objection to. She seems proud of them when she talks about them to strangers, just not to them.

The middle kid in particular has started to take vocal objection (to me; dad and MIL have a difficult relationship and they won't speak about difficult issues to him) to her perception that cousin is treated "like the favourite". Cousin is never criticised and is also praised more to them than they are ever praised. At one point she was called "my most special girl" in front of my girls. They obviously said nothing but they did tell me later they took objection to that which I understand. She is also given more attention and "the special place" at family occasions (including my FIL's funeral at which she was specially chosen to sit with my MIL. Now obviously MIL had lost her husband and
I would not dream of criticising someone in grief. But it did make my children feel a bit off as cousin had only known FIL a year at that point and obviously they were upset about their granddad and were made to sit on the other side of the church and not acknowledged by MIL.)

At one point a while back MIL confided in me that she feels less secure in her relationship with cousin and BIL's partner because she perceives that relationship is less stable and much more likely to break down. I understand the 'eggshells' thing and I don't hold that light touch against her at all, it is a difficult situation, but am I wrong to think the answer could maybe be to be a little nicer to all the grandkids rather than treat one as special?

I do get treated appallingly differently from BIL's partner, but I am also a grown woman who has been dealing with MIL's behaviour towards me for decades and (without meaning this unkindly) I've got a mum of my own and am not bothered about how MIL feels about me at this point. I am sure I am not the DIL of her dreams but she's not the MIL of mine either, we make do with what we've got.

We honestly get along fine, I have her over for dinner etc, I text frequently to check in, I take the kids visits without husband there and stuff. We don't have any trouble or strife. It does give me a laugh when my birthday etc is ignored though and my SIL is given cups of tea and stuff whilst I'm sat there ignored. Whilst this genuinely doesn't bother me, the kids have also picked up on it and several times cousin has taunted my kids with it.

Anyway. Sorry for the novel. Does anyone have any advice on how I can deal with this issue? I feel like I don't have any good personal perspective to help them with this. They see her frequently, there is not an issue of low contact or anything, they are just feeling that she 'doesn't really like them' and 'cousin is the favourite'. I do not know how to handle this. I am afraid to say I was my own granny's first grandchild and whilst she was loving and strictly fair to us all, I was by far the oldest so we had a different and very close relationship. (Okay, I was older than the rest and the first one, I was the 'special' one, I admit it, but it was nothing like this. It was just different from the 'little ones'.)

The thing I struggle with is, I don't think the kids are in any way wrong, she DOES treat them differently, but I also feel some responsibility to try and maintain this relationship for them. They are getting into the teen years where if they don't feel like maintaining that relationship, they won't really take over that investment in it and it will fade away. I know this would upset her greatly (it truly would, I'm not projecting) but I don't know how to deal with this. Particularly in the sense of, what do I say to them to try and get them to give her some grace?

Any help? The whole thing is incredibly awkward and my husband gets angry with me over it because he doesn't want it to be awkward but will take no role in addressing any of it. Like I say he has a very difficult relationship with her and becomes angry even when she is mentioned. He is also clear he will not address how he feels about that.