I probably should have put more detail in the OP but it would have turned into an essay and I am actually working between browsing MN and stressing about how I am going to manage to sleep with both Chis.
DD has been ill since she was in primary school. It started getting really bad when she became a teen and has been slowly going downhill since. She is getting help. I have been fighting for her to get more help/the right help since she was 10. I appreciate that posters mentioning her mental health are trying to help, and thank you, genuinely but I really only wanted to know whether popping a dog into her room might cause serious health issues for her date or whether it would be really terrible to demand DD2 take one, which is why I skimmed over mental health issues. It wasn't because I don't think her issues are not serious or that I am not trying to get her the right help.
The date is a friend of her friend's boyfriend. She's known the friend since she was 11 and his boyfriend has been in the picture for about 2 years now. The entire family has met the friend and the boyfriend numerous times. The friend and the date have worked with each other for about 4 years.
DD1 and the date met at a party about a year ago when she was still with her last boyfriend and have chatted on and off online ever since, in group chats with other friends and 1 to 1. It started becoming as romantic as an online-only relationship can be a few months ago.
This is the only man apart from the friend and his boyfriend who she has ever invited to stay at the house. If she was regularly bringing strangers into the house for sex I would be worried but she is not. If she starts trying to I will act on it.
They've been sitting in her room watching movies with DD2 and her boyfriend up until an hour ago so I don't think he has come here just for sex. I do believe he wants to spend time with DD1 getting to know her, although I am not completely naive. I have made sure there are condoms in the bathroom.
I only mentioned her mental health and inability to form relationships outside of the house to explain why I didn't want to kick up a fuss about her dogs in front of her date.
She is getting help, and has been since she started displaying symptoms of poor mental health and now I am aware she is feeling completely unable to leave the house I will make sure her mental health team is aware.
I walk her dogs. I make sure they get appropriate enrichment during the day (or night depending on when I am awake). Her dogs are very well cared for. They are a lot more spoiled/babied than I would like but they are walked and they do get played with and have mentally stimulating play and training every day.
I call them rats as a joke. I'm actually quite fond of them, especially rat1. Rat2 is a bit dim and doesn't have much personality but I do not dislike him. I also call DD2's cats cunts. Neither the cats nor the chihuahuas seem to mind 
If this guy doesn't learn to love her dogs I can't see him lasting long. She is already complaining that she cannot have her oldest chi in her room because she is the one who cuddles in bed with her. If she has to pick between her date and her dog, she will pick her dog.
Anyhow, the rats sleeping arrangements are sorted now and I am due to finish work so will be off to walk them all shortly.