I had similar problems with my MIL.
I couldn't stand her being around after the birth of DD1- it felt like invasion of the babysnatcher! She also did the guilt trips- we didn't drive so were at their mercy regarding visiting. A couple of hours was long enough for me but MIL wanted us there for lunch and tea... she cried that she wasn't a proper grandma, made sarky comments etc.
Can feel my BP rising as I remember this!
I acted like a massive brat in response. Just stomping about, leaving the room as soon as I could if she visited, not really talking to her etc.
Things only got a bit better when I had DD2 12 months later, and when DH told his mum that I had depression and she should back off a bit.
Now it's 3 years on and I actually get on really well with MIL
yes she's very different to me and we both went about things wrong at the start, but she is a very good grandma and loves my DDs, so that's what I focus on. Things that I find irritating about her, the kids love! And also, once they got mobile they could quickly crawl/ toddle away from MIL if they didn't want to be picked up and slobbered over
which put me at ease a bit!
DD1 was MILs first grandchild, and she just had different expectations of the grandparent role than we did.(I'm from a bit of a dysfunctional family myself so wasn't expecting the level of involvement she was).
The only advice I can give you is that is does get better in time, and your MIL will be a loving presence in your DDs life. Make sure you feel able to say no, if she wants to hold your DD at an inconvenient time, but also make sure she does have time to hold the baby and bond.
I think DIL and MIL is one of the trickiest relationships there is! Good luck.