"I imagine if she posted here to say DP's ex is insisting that she has a meeting with me before letting DsD say the night in the same house as me, the responses would have a rather different slant."
The response would depend on who posted, it hasn't been everyone agreeing even on this thread.
My response would be along the lines of 'you are going to be in this child's life, in a position of trust with the child. It's just a quick coffee/meet & greet it won't hurt you to do this and will make relations & communication among all the adults in the child's life run more smoothly. It's a small thing to do to put this mothers mind at ease. And you never know you might find it useful to be able to talk to her about the child at times if you need to.'
"Not a valid comparison, she isn't being paid to take care of you DD she is your Ex's new partner" I agree it's not a valid comparison, nursery teachers are vetted and background checked, have training and experience, are unlikely to be left completely alone with the child or have the responsibility of caring for them overnight. The ex's new dp could be anyone!
Also those saying it would be uncomfortable or awkward - are your feelings of discomfort more important than a child's need to feel secure that all the adults in his life can put their feelings of what is really just embarrassment aside in order to ensure THEY are best cared for? The child/ren are more important than a half hour of discomfort for you.
And yes if it's a new partner moving in with RP the same applies.
I'd be very interested to know if those saying there's no need, it's unreasonable etc have actually been in op's position? I have and from what I've read of the responses generally speaking those saying op is not unreasonable have and those saying it is unreasonable have not.