If you get on great with your MIL now, for God's sake keep it that way and make absolutely sure she does NOT stay for more than a couple of nights in the first three months, and absolutely NOT until you feel up to it after the birth itself.
It's a very precious but also difficult and challenging time. And also, it's YOUR time, for the first time, as a new family. Even if you actually feel great, and confident, and physically ok soon after the birth, you really really will RESENT someone other than your DH and baby muscling in on that really special, personal time. You will hate her being there, even if you love her, so don't let it happen.
You really need to make this clear to your DH - that it's not his mum's place to be around during the majority of this time, that it is likely to damage a good relationship if she does, and also - why does he want that? Make him think about it and talk honestly about why he is so keen to elbow his mum into your first few weeks as a new family, his NEW primary family unit. Make it clear that he will be needed in those first weeks, by you, more than he has ever been needed before, in a most intense and personal way. It would be impossible for him to fulfil this role as your husband with someone else looking on, needing conversation, someone not within your partnership. Totally inappropriate. And you will also need your personal space in a way you have never needed it before - to wander round, boobs out, at 3am without worrying about a houseguest, to not shower for a week, to eat odd meals at odd times, to cry and be moody and tired and emotional and unreasonable. He will be all those things too.
He needs to talk to her now. If she's as nice as you say, then she WILL understand - she's had children herself - and if the grandma broodiness has taken over and she doesn't want to take no for an answer, then make damn sure you put your foot down even harder, because if she's shaping up to want to be IN THERE and DOING STUFF with your baby, then it's 100% certain that you will end up falling out massively.