This is really a tough call. On the one hand, the woman gave you your husband, obviously she needs to be honored. On the other hand, she's using guilt to try and get her way, rather like a large child.
Having had my share of grand-parental issues throughout our marriage, I'd truely say pick your battles. Again, while speaking out of both sides of my mouth, establish you're the mommy this time around, so she needs to please respect your need to be with your own daughter. On the other hand, if your daughter will not be harmed by your in-laws, there's no harm in going out to run some errands or have a drink while your inlaws are tending to her at your home.
Sometimes it's give and take, but make sure you make it clear it's not a trust issue, you're just not ready to leave her. If you say you're not using babysitters yet, that is a little impersonal, they're more than sitters, they're family. If you say I am not ready to leave him/her then that's your issue, not theirs. It's subtle, but important. Especially if you say something like "How could I not trust and love you, you gave me my husband, the father of my baby. It isn't about you or your abilities, it's about me and my attachment to my baby."
Take the fall, otherwise you'll NEVER, ever hear the end of it. lol. That way you get to have your way and spare their feelings. Get used to being the bad guy, you're a mom now! lol.
As your child grows, they'll be some fantastic allies! Causing hurt feelings in the beginning can make things difficult later. And yes, I speak from some serious experience here!