My kids are only 5 and 3 but it will be a long time before I leave them at a party or playdate. I think of playdates as mommy dates too. I invite the kid and mom over with an invitation for "coffee and a chat" while the kids play. Perhaps you could invite them to your place? That way If the mom doesn't want to stay at least you can keep an eye on things.
I don't think you're strange. I am super overprotective too, and don't even have a good reason for it. I just am. I pulled 5 year old DD out of sparks because I had a problem with all the sleepovers and other activities I had to leave her at.
wife of my soldier Steve, mama to my beautiful girls Rowan (11/07) and Linden (03/10)!