I wonder what the reaction to this thread would be if the OP had complained her DH was bringing over his sick mum/sister/best friend ? Chances are there'd be less of the "oh but everyone needs some TLC" and "you wouldn't ship your own child out if they were ill" comments and more of the "FFS, they're an adult, best stay away until recovered" remarks.
FWIW, the OP's stepdaughter isn't being "shipped out" as she already lives elsewhere - as many adults do. Clearly, most people wouldn't ship out a child who lives with you all the time - to where exactly? - though having said that, my MIL very kindly (and sensibly) held onto my DC for a few extra days years ago when they fell sick while staying the weekend with her so the possibility of infection spreading elsewhere needlessly was minimised ....
.... which is what this thread should be about, regardless of the relationships involved. The OP even said that her DH hadn't told her that his daughter had been vomiting (until, I presume, she'd already arrived) thus preventing OP from potentially taking sensible precautions and/or trying to keep much younger children away from older adult child. Which is very stupid and selfish on DH's part.
Okay - yes, it's nice to be nursed, hot drinks, baths run and so on. But most adults would manage on their own if they possibly could and if they really were extremely incapacitated and genuinely needed someone to help them would understand they should keep away from as many other people as possible. It may well be the adult patient in question here is rather young and perhaps hasn't thought this through when her dad offered, but he should certainly know better and it's damn rude, apart from potentially unpleasant/miserable or even dangerous to expose your family to possible infection without even discussing it first. The best option as others have said would have been for him to visit her while paying attention to hygiene etc.
I too would be very very angry about this .... especially just before Xmas which is the last time anyone wants to be sick.
On a similar-ish note, one of my DCs had severe D&V (again) a while back - projectile vomiting, over and over - really nasty, had seen out of ours doctor - and my DP's ex still insisted that his older DCs came here for their usual visit as she wanted "her time". How bloody irresponsible to expose them to that. However, DP IMO could and should have refused to have them - which would have been easy as he has to make the 200+ mile round trip to fetch them - and he didn't. I was furious with the selfish pair of them - for exposing the kids unnecessarily, but also for him being out of house for 10 hrs plus that weekend leaving me to cope and clean a child (plus bed/carpet/sofa/me - at one lovely point I had DC's vomit in my bra) who was being sick so much. Really really selfish.
The relationship here shouldn't influence common sense.