Should I allow it?

So for multiple reasons (bad mouthed my mum, said she felt hurt I bought my own double buggy, told my pregnancy news to her parents when we said keep quiet, tries to force us to see her parents regularly and guilt trips when we don’t etc) I dislike my partners mum. I had a good relationship with her previously but since she bad mouthed my mum in November 2022 I have gradually just wanted less and less to do with her. I still let her see my kids every other week and went for her own Christmas Day but I don’t want to volunteer anymore of my own time alone with her and the kids (she keeps wanting to go to play cafes without my partner). My son is turning 2 soon and I have a 7 month old daughter, I’m a bit of a recluse and don’t really go out with friends anyway except when we socialise with our babies and with my friend with no babies I bring my babies anyway. I look after my kids 90% of the time and the only other people I trust with my kids is my mum and dad (we lived with them until my son turned 10 months and my mum is like a second mum to him) so naturally my mum is my go to if I just need an hour to food shop or whatever. My partners mum joked before I had my son with her friend that she wouldn’t babysit because I never go anywhere but when my son turned 1 she told me she is upset that he’s 1 and she’s never had him alone, when she’s looked after him in our presence she’s let him go in cutlery draws and when pulled up said ‘well I had my back to him I couldn’t see’ and would leave him on the sofa when he could roll or let him crawl to the hallway with no baby gate on stairs. My kids are my world and I don’t trust her ability. Now my son is turning 2, she is obviously feeling sorry for herself again and yesterday said when are her babysitting duties starting and I must let her look after her grand baby’s. I just replied ‘yeah’ and didn’t say anything else. All my feelings aside, I’m questioning if I should be letting her babysit even though I don’t need her, my mum babysits out of helping me not because she wants to but my partners mum wants them because she wants them. My partner doesn’t care either way, he wants to move abroad so doesn’t care about her spending time with our kids but his mum is very jealous over my mums access and has made multiple comments in the past. Too add, my partner is an only child and she is single.