It is so manipulative of her to do that. and for her husband to agree to it does not bode well for their marriage. I would not tolerate this.

And at this point, I'd personally force my husband to pay two months at a short-stay hotel if necessary to not have her my house while she "job hunts."

She will be difficult to get out of the house. And limiting it to two months or whatever does not help. She is stealing their private time with their new baby as new parents and they'll never get that time back.

It's already caused OP too much anxiety when she should have been enjoying this time adapting to her new baby without MIL getting in the middle of it.