If she was still in receipt of DLA, then she must have been under 65? So it would be financial abuse of a Vulnerable Adult, perhaps, but with the sums involved, the CPR wouldn't proceed, tbh.
If MIL was her NOK, then unfortunately, she had the legal right to deal with the funeral, DC etc. On that basis she claimed the funeral payment. They do ask if there is anyone in the immediate family (that includes the OP and her DW) is working and could cover the costs, so a declaration has been made that there wasn't.
If the Uncle is on a low income, I don't think that an offer to pay it at £5 a week, is unreasonable, tbh.
It's up to your DW if she wants to go to the Police, it doesn't matter what anyone in here thinks, this was her Gran and is her Mum (although a shit one).
If she doesn't want this and you push for it, you'll be the one causing her further upset.
My Mum died in September, I informed DWP, but didn't follow up on other things until November. I'm starting Probate in a couple of weeks. There isn't a legal time frame for that.
The death of her Gran will make it easier to distance yourself from the rest of them, so this drama will come to an end soon.
Your MIL has acted in a way enough to go NC, she's done you a favour.
If you don't want to pay the £800, then don't, but your DW can, if it's important to her.
Personally I wouldn't, unless this amount means very little to you.
Not my Monkeys, not my Circus, certainly does apply to that side of the family.
I hope you've made Wills etc.