As it's your MIL I'd be getting your DH to have a strongly worded conversation with her. My DH does this really well with my mum actually. He will say you know we love that you love DD so much and want to get her things but she has so much stuff and she doesn't need anything so you need to stop buying for her. It's an ongoing battle though.
I would put some of the gifts aside. Tell MIL that you appreciate them but you don't want them getting 'lost' and forgotten in the midst of all the other presents and that you'll have them aside for later when they can really appreciate them more.
We've spoken to my mum numerous times about not buying stuff for DD. We have to keep at her about it as otherwise she just does it even though she knows we don't want her to. DH is pretty peeved at the moment and going to ask her for receipts for stuff she's bought and take it back
This might seem harsh BUT she does not listen and has wasted so much money on things that never get used because she refuses to buy DDs size. Since she was born (17 months now) my mum would have spent at least $300 on clothes for her and out of all that DD has probably worn 5-6 things because she never buys anything that fits and then by the time it does fit it's the wrong time of year (think winter coats or thick pjs finally fitting in summer= useless). The other day she bought her clothes in size 3! She is in size 1 FFS. And when I said it won't fit her for ages and probably be the wrong time of year when it does fit she tells ME not to be ridiculous and she'll grow into it quick. She honestly thinks DD grows out of clothes in a month or something (she did this when I was a kid and had me in size 16 school uniforms when I was a size 8 as a teenager. I never 'grew into' the size 16 ).
It is so wasteful as I end up having to give the stuff to charity completely unworn and I've told her so many times and she doesn't listen she also does not have the money to waste, I just wish she would buy 1 nice thing instead of all the stuff she buys.
For gifts at birthday/Xmas I usually let her know a couple of things we'd really like DD to have and try to get her to limit it to that. But I know she has bought a few extra things, which probably won't fit or be age appropriate so get shoved in a cupboard it's an ongoing battle here. Mum still goes crazy but it's less than it would be if we weren't constantly asking her not to.
DH set up a bank account for DD a year ago and gave the details to my mum and said why don't you pop a few $ in her bank account when you want to do something nice for her. My mum does this which is good, makes her feel like she is giving DD something regularly I think. We are going to give DD the money when she's 18. Would your MIL be open to something like that instead of the physical gifts?