Several issues here OP. Firstly, as flapjack says, you need to prioritise your daughter's settling in above and beyond anyone else's wishes. I didn't let anyone stay over with us for a few months.
Secondly, local authorities are a bit inconsistent, if their policy is no one stays without DBS (old CRB) checks and you have people staying without telling them you are in a tricky position. You really don't want to be getting into unnecessary conflict with them.
Thirdly, although totally honest with our local authority about who stayed with us, who visited for us 9 years as a foster carer. Suddenly, after 9 years we were informed that anyone who stayed overnight (even if never being left on their own with our DC for a moment) had to be DBS checked first. That was a few days before we had relatives due to stay who ended up having to cancel their plans at the last minute.
But the main thing is your daughter. This is not the same as having a birth child. Your MIL needs to accept this. There will be many years ahead when relatives can visit and stay but I would keep it quiet and calm for your daughter this year.
Also, as flapjack says, you can hide behind it being a condition set by the sw that you're not allowed overnight guests yet.
Congratulations btw! How old is your daughter?