Don't give up yet! I have been reading about DL alot recently and I swear in my reading I did read about a kids club. I am sure somone with more DL experience will post soon, but if I find out where I read it, I wil post!
I researched this a little, and it looks like the only kids club is at GCH, like Terry S. said it's called Pinocchios Workshop. They say it's to give mom and dad a night out, so it may be just what you're looking for. However, it's for kids age 5-12, so hopefully your kids are in that age range. Mine unfortunately are not (we have a 5 year old and a 17 month old). I guess nobody likes to change diapers. (Peeyew!)
Anyway, that's all they offer except in-room babysitting services. I don't know about you, but I wouldn't hire someone I don't know from a babysitting service I don't know to watch my kids in a hotel room. At least with a Disney owned and operated service like a kids club, you know your kids are safe and having fun.
Too bad they don't have a toddler club. I'd be willing to pay extra just so my husband and I could have a couple of hours together for a quiet dinner. (sigh) Oh well.
My daughter went to Pinocchio's workshop this past August. She loved it and she has attended a lot of kid's clubs. Last year she went to 5 kids clubs when we were in Orlando. So she is seasoned.
They take a picture of you and your child when you walk in and she can only be picked up by whoever is in the picture. A bonus is that they send it home with you. We paid 12 an hour and we left her there for the maximum which was 4 hours. You can buy dinner for your child for another 4 dollars. Your kids can stay and play here only if you are a guest at one of the DLR resorts ie Grand Californian, Disneyland Hotel or the Paradise Pier Hotel.