To give you a little perspective...
My mum and dad were together for 32 years, since my mum was 16. 9 years ago my dad dropped dead.
Grief made my mum completely insane. She said she saw no point in living etc, very similar to your MIL.
My brother and I had lost our dad but in her eyes she had lost her whole world. My brother and I still had partners, friends etc whereas my mum felt she’d lost all of that.
She was incredibly selfish, bizarre in her behaviour and I actually felt for a long time I had lost both of my parents the day my dad died.
However, she came back around BUT only because we allowed her to grieve. Her pain must feel overwhelming and all consuming at the moment.
Judging her or “laying down the law” seems cruel. She lost her husband so recently I think you need to show some compassion and kindness.
Your DH can assert some healthy boundaries though. I used to say “Mum I’m here for you but I don’t want to hear you say XYZ. I’m grieving too and I cannot emotionally support you completely”.
I also got her to see a grief counsellor. It helped her immensely.
What do you think she’ll do to your child exactly?? My mum was and is a fantastic grandparent. Her grief was irrational at times but I didn’t for a second think my child would be in danger with her.
Also showing pictures of her deceased husband to her GD is not weird or wrong.
You sound very judgemental.
Imagine how you’d feel in a few months if your DH died now. Be kind