Hmmm
I wonder if you feel that she’s co opting your “thing”? Did she only come up with the idea after you discussed yours? Is that the problem?
I actually don’t think that there’s anything wrong with wanting a special unique reminder of your baby’s first days, something that only you have.
I have a box of a few baby clothes from each child, I would be 

if either my DM or MIL asked to share them.
I would say no without question.
And it would be nothing to do with not getting on with them or not appreciating that they love my children.
There’s a couple of options. Which you take probably depends how much of an issue your MIL is going to cause about this and how much it’s going to upset you to give in:
Say no politely
Acquiesce and give her some clothes.
Buy some second hand baby clothes and give her those.
Give her some clothes to make a blanket and do something different for yourself, eg have a teddy made or a wall hanging.
In future don’t discuss this kind of stuff with her.