I was recently a new mom, myself, and I agree with pretty much everyone that those first few days can be very stressful, and both you and your husband’s comfort should come first. It looks to me, though, that even though your husband agreed to talk to his mom, he’s not entirely on board, and that strikes me as a problem.
First of all, I wonder how you explained your request to him. Given that he’s very close to his mom, and hurt that you’re not as close with her, I imagine you might have tried to make it all your “fault”, as in: “I’m just afraid that I’ll be too tired and busy to be a good hostess to your mom, and I would hate to inconvenience her.” If so, it makes sense that he would reply as he did, “Oh, don’t worry about her, she’ll just make herself at home!”
But it sounds like that’s exactly what you’re concerned about: that MIL and BIL will act like they’re at their own house rather than yours, and end up being in the way and/or making more work for you. If so, I think you need to say that to him. Don’t say, “I can’t be a good hostess,” say, “I’m not worried about having to entertain them; I just want to be able to have privacy if I need it, or to have some time alone with the baby, or to take a nap. I’m not worried about having to cook and clean for them; I just don’t want to try to grab something to eat and find that there’s no food in the house, or that there are no clean dishes.” And so on. Explain to your husband that it’s not personal; you would feel comfortable telling your own family to leave, or to clean up after themselves, but that you don’t feel it’s your place to say these things to his family. And perhaps, offer that if he’s willing to be the “bad guy” in that regard, then you could be more open to them staying with you.
The thing is, if he’s not really on your side, then that may well come through (either explicitly or implicitly) in how he presents it to his mom: “Chipmunk just doesn’t feel like she can handle having guests. I don’t know what her problem is; I tried to tell her she shouldn’t worry about you… etc.” I also think that he shouldn’t be telling you anything about her reaction, other than perhaps, “She’s not thrilled, but she’ll go along with it.” No good can come of you knowing that she said she “felt sorry for you”. He should be presenting this to her as, “This is what we want,” because if it’s not what he wants, then he shouldn’t have agreed to make the request.
And I’m curious about your statement, “My husband sounds like he wants her there and it would certainly make things easier for him.” How so? If she’s actually going to be helpful to him in some way, then you (both) need to take that into consideration, and weigh it against the fact that she’ll also be a hassle in some ways. But ultimately, it comes down to baby’s needs first, yours a close second (ahead of and not tied with your husband’s only because you’re going to be going through a lot more physically than he is), then husband’s, then everyone else’s.