When I posted this question, I didn't expect so much savaging and lack of understanding by other mums. I am taken aback by the reaction. I didn't think it is such a big deal leaving my child to go on a playdate.
My daughter didn't just turn 3. She was 4 and some kids go to Reception by this age!! So why is there a different protocol for school Nursery kids and Reception year kids? Many mums have their friends kids after school for playdates.
Joyfulldeathsquad You are very quick to judge and condemn someone who doesn't fit your mould. I don't think I left my child to the other mum for cheap childcare in anyway shape or form. The playdate was only for ONE AND A HALF hour at most. No, I wouldn't have left my child with the other mum if the playdate was in a park because I know that she can't be held responsible in a PUBLIC place for my child! For the fact that there are other people around and my child may wander off. But the big difference is, my child was on a playdate with her friend in their HOME - which I don't expect total strangers hanging out or her to go missing.
Before which, I had made sure that she had already done her once a day poo business so there was no need her to poo, hence for the other mum to wipe her bottom. That said, she already knew how to wipe her own bottom. So I didn't think she was going to need any more than a little wee.
BESIDES , the whole point is she was there to play with her friend. In my mind, I felt I wasn't putting my daughter there for them to really care for her for a long time e.g. daycare where the carers were there to educate/ care for , put her to sleep, feed her???? Okay she had lunch there, but she didn't need anyone to spoon feed her.
Given all the mums savaging me, I asked myself why I was so unsure of staying in the first place. Well, upon reflection, the original invitation to me by one mum states that "Would my DD like to come over to play".
THE POINT IS SHE DIDN'T FIRST ASK "Would you(my name) and DD like to come over to our house so DD can play with her DD". I felt that when she did casually asked me in for tea later at her doorstep, I then interpreted that as she did it purely out of POLITENESS. Similarly, the other mum also said "Would my DD like to play with her DS and have lunch there".
If they wanted me to go, why didn't they include me in the invite first?
So in my mind, I felt that they weren't actually that keen for my company in the first place.
I have friends who asked if both me and my DD would like to come to their house and I would have felt more comfortable thinking they actually wanted me there too. 
For those who react badly:
I don't think I knew them well more than seeing them almost everyday dropping my daughter off at the state school nursery (not a daycare). But total strangers...NO! I guess I thought they live locally... have kids in the same class as my daughter... they have my mobile...I have theirs..so why is it so offensive to be leaving her with them for 1-2 hours for a play with their kid, since they had so asked?? Why hasn't anyone said it is also offensive to leave your kid at a birthday party at the same age?
So many times does one have to go along before it isn't offensive to leave your child with them when they asked for your child's company to play? Why would subsequent playdates not be deemed as cheap childcare by other mothers if you did leave them?
And NO, I didn't do a quick handover. I chatted with them before and after the playdate and I also walked their children with my own DD to school after the playdate.
I haven't asked their child over yet purely because of their cold treatment to me after that. I was totally puzzled and unhappy. 