OP - it sounds like you’ve fallen in love with an ideal.
Yes he is nice personality wise, but the rest doesn’t work for you - his friend and daughter. Which means this relationship doesn’t work.
He is well within his right to have a female friend, after only 6 months you cannot put restrictions on that. You are well within your right to not like it, once you’ve mentioned you feel uncomfortable and that’s been ignored then clearly neither of you are compatible.
In future I’d have the ‘talk’ before investing so much energy in someone, ask ‘what is this? Are we a couple, exclusive etc’ because making assumptions on the basis of Christmas and daughter introductions doesn’t cut the mustard.
I agree with the rest, no need to autopsy, if you see him a breezy ‘hi, how’s the kid got to dash, bye’ will suffice.
It’ll probably only be awkward the first time anyway.
Going forward I hope you meet someone who is nice. This man sounds like an arse.