If his wife was suddenly taken ill with something potentially contagious, I think he should have texted you - not to announce his arrival, but to let you decide if you wanted to cancel due to the child potentially carrying a bug.
If the child was nervous being in other people's homes for the first time - I think that should have been raised when you were making the playdate with the mum. Lesson learned for next time - don't rely on the other parent(s) to bring it up, ask about it yourself.
If the wife was suddenly taken ill with something non-contagious - say nightmare IBS - I don't think anyone had any good options, TBH.
There might not have been time to get in touch without being hideously late, they might have not wanted to let down either/both child(ren)... the child might not ordinarily have been clingy, but extra needy due to her mum being sick and reacting to that...
I hope the girls at least had a good time.
I think you're obviously entitled to feel uncomfortable having a strange man in your house - no one has the right to dictate how you should respond to your trauma. But maybe it would be better for you to organise play dates away from the home until you get a point where you do know both parents and it does feel less awkward?
With my good friends, very occasionally a partner will come along as well (it's rarely to switch, but it does happen). One of the couple is my 'main' friend and the other one is my friend through association, but they're both friends, and no one on their side minds. The couples aren't joined at the hip, but there's also no reason to exclude them from something unless someone has explicitly organised a meet up to talk about something deeply personal.
I don't think many parents would think much of switching which parent was taking a child to a playdate - they would be be trying to make sure the child got to the playdate. So, to protect yourself from situations like this recurring, I do think you should host few things at home until/unless you feel more comfortable with the family.
PS I'm sorry some man in the past put you in the position where this is all even a consideration. You might feel like you're making a big deal out of something you shouldn't and/or some posters may say or imply that... but you've lived through something, and you shouldn't have to pretend you don't have those feelings while you have them. By organising playdates for your daughter, it's clear you're trying to make sure she has a nice sociable life, so it's very obvious you're doing what you can to make sure you're not passing on your trauma. You're doing great in looking after her needs. It's OK for you to have needs too.