I didn't necessarily know the kids' parents, but generally in kindergarten, the parents would call to invite the kids over. That gives you a chance to "meet them" over the phone. You don't have to interrogate them, but if you are planning to pick your daughter up, then at that point, you will meet a parent face to face.
Maybe some of the moms will have some "stock" phone interview questions. You could tell the other mom that you are new at this, and don't want to interrogate her, but would like to know what her child's after school routine tends to be like, what she likes to play with. Looking back, I don't think my girls went anywhere during kindergarten that I would have, in retrospect, wanted them to avoid. In later school years, there were some questionable homes along the way, but only 2 out of 4 children. (so far) And with the 1st one, we tried to do more inviting than sending, because we really liked the little girl, there just wasn't appropriate adult supervision, and they drank a lot. With child #3, she decided she didn't want to go to that house (both of these were for staying overnight) anymore, which made us very happy.
The thing you CAN do, to ease your own mind, is to make the 1st play date a bit shorter. I assume the other Mom will pick the girls up at school, and you can come by an hour later, or 2 hours later to pick her up, due to "family scheduling", or because it's convenient with your work schedule. Whatever works. Once you pick your daughter up, you'll have checked out the neighborhood, and you will meet the parent, so you'll have a better opportunity to "check things out". Also, remember, that kids are most comfortable with kids who remind them of home -- people who are kind of "like them". They are also very accepting, so it's not always true, but mostly they will make friends with people who are similar to them. (if that's any comfort)