I haven't been in that situation, but if DS or DD didn't feel comfortable sitting on a strangers lap - then I wouldn't want to force them to do it!!!!

I think it seems a little unreasonable to expect a 2 year old to be fully comfortable with them straight away. I know DS sits on the carers laps at daycare but he's been there for a while now - and wouldn't have done it for a few weeks I would imagine!!!!

I hope you figure out a solution soon.