This is particularly MIL and his Grandmother. We have a 6 month old DD and bought our own house at the end of last year. DP and his MIL have had a difficult relationship, so he tries his best to please her (sometimes too much)
Throughout my pregnancy MIL barely spoke to me unless it was about the baby (which was weird, we had been close before). For example she'd ask if she could come to midwife appointments to hear the heartbeat, come to scans etc and when I would politely say no thank you I just want DP there (even the birth) she would ignore me/be off with me and play the victim to DP saying that I was selfish and she had every right to as it was her grandchild. You'l see a pattern of this, she ignores me then drives a wedge between me and DP.
Ever since DD was born she would turn up without notice, bring things from car boots - a pram, toys, clothes, literally anything, in her own words because she's the 'favourite' Grandma. She always jokes about this to DD who obviously doesn't understand but I don't want her to keep doing this as she gets older. She's insanely jealous of my DM, often joking to DD that my DM isn't really her grandma 
In the early days I would let her take DD out for a few hours so I could sleep or have a shower, it was a real lifesaver and I'm grateful. But now she wants her all the time. Constantly asking to have her overnight, on christmas Eve, on my birthday and when I say no she is straight to DP with a pity party saying his siblings (both under 10) are heartbroken, it's not fair etc so then he falls out with me and argurs that it's "only" one night. I'm sick of saying no and having his whole family just be plain arsey with me. MIL apparently called me a nasty bitch to SIL because when SIL(7) asked if my DD could sleep i said Sorry but she can't, because she needs to be with her mummy and daddy, she's only little.
Me and DD went to visit his grandmother (without DP) and she asked "has DD been MILs this week then?" I said no why, she said "She wants to have her for a few days to give you a break. She's off work"
All i keep saying is no, I don't need a break, I'll bring DD round instead and have some lunch with you. Then she ignores my messages/phone calls and moans to DP about how selfish I am which in turn makes him be funny with me and sometimes argue with me.
When we go round as we leave she will say to DPs little sister "ask if DD can stay a bit longer" as if to make me feel guilty for saying no to a little girl. I'm really dreading christmas as we've agreed to have lunch at her house then visit my DM. But MIL is insisting on having DD overnight on xmas eve to which me and DP have both said no and she didn't speak to us for a few weeks.
I don't think I can take much more of her constantly and daily trying to take DD off me, and DP being too scared to disappoint MIL. I can't imagine a future like this