I don't talk to someone about childcare until I've already talked to at least one reference. Just how it's worked so far. For me: I have a list of people that are my "running references"....my resume says "references are available upon request" and i have a list of references who have already given me permission to hand out their information (just name and a number, along with what type of reference it is--personal friend, former supervisor, coworker, etc). I'd suggest having a few references on hand, permission already given.
For me: when I was providing childcare, I encouraged parents (both) to come to the house to talk to me and my husband together as well. Providing in home childcare, I felt that I was interviewing them as well as them interviewing me. We let the kids play, they could tour the house, sit in the living room and have a little talk about how we do things, what are they looking for, etc. I always said "If you like, I can give you references" (noone took me up on it though; they spent time in our house, an in-depth conversation with both of us, watched the kids play, etc and knew by the time they were leaving). I suppose that my offer to give them references was AFTER our interviews though....I always push for people to come over and meet us as a family. If they need a reference after that, of course they can have some.