Re: Play date etiquette ??
Maybe this mom is in the same situation as you and trying to make friends with you and each of your DD being in dance is a good ice breaker.
Personally I would call the mom up and talk to her. Tell her your concerns and see if you can agree to a different location, your house or a park or playground where the kids can play and you two can chat. Explain that for the first get together you are not comfortable leaving your DD. I am sure she will understand especially since she doesnt know you either.
wife and mom
~If you see a bunch of types I am probably NAK on my tablet in the middle of the night. Please excuse them.