I know how you feel OP. My PiL are French where this is very much the done thing. They suggested we should leave DC with them overnight under when three months. Obviously I politely declined.
DC is still under one, but DH has floated several times that they would 'love' for DC to go to PiL's (in France) to stay for the weekend 'as soon as DC is old enough'. Think their opinion and my on what is old enough may be very different.
For me, it is tricky as a big part of this is cultural. As I understand it, many French parents leave their young children and babies with their parents / PiL for up to a week. I know of two examples of DH's friends leaving their babies with Gps for up to week at under 9 months.
I would not dream of this. I can imagine we will get to it one day, but that day, for me, is when DC can understand and be enthusiastic about such a plan, which could well be a good few years off.
It has also been pitched to me as giving me a 'break'.
Can you discuss direct with your MiL/ PiL? I suggest first off you see if you can get her to articulate why this is so important to her. Take that away, and see if you can understand where she is coming from (which is not the same as agreeing with her / agreeing to do it).
Then maybe see if you can offer something less / else which helps give her some of what she wants, stepping up to longer stays as your DS grows up? Dangle in front of her that she needs to build your confidence, incentivising her to work with what you are offering in order to get more alone time with DS.
The concern for both of us, probably, is that by saing no it becomes a 'thing'. Can you articulate to her that 'no' now doesn't mean 'no' forever, but 'not yet'?