I have no qualms about asking someone to leave my home. That is my sanctuary, and if I feel like someone is invading my space, they must go. You can do it without being rude.
The burden cannot fall solely on her or even you. He has to be willing to voice his needs, too. You said in one of your other posts that he called what you and him have "just sex" or something along those lines. Red flag. If you have stated your needs, he has to be willing to at least compromise or be strong enough to do what he sees fit. He knows what a relationship needs to flourish. I remember that you were not entirely comfortable with the idea of being in the closet. I cannot remember if he asked you not to say anything or how that came to be. You have already stated that being in a relationship where you have to be the secret is not something you care to do for an extended amount of time. It might be working now, but it can turn into another problem.
He has time alone with her, and obviously, you are going to want/need time alone with him. I realise it is still fairly new, but is she uncomfortable with the idea of him being alone with you? It would like a constant third wheel. I would not want to always have a third person around almost chaperoning. I am too old for that, and I am not in school on a trip any more, so I do not care to be chaperoned.
I know you mentioned the parent issue. He is a grown man, and if he wants to stay out all night and his girlfriend does not have a problem with it, why should the parents? Did she need to be eased into an arrangement like this? I remember reading a few of your posts before, but I cannot recall all the details.
I would suggest sitting down with just him, then her, and then the three of you. Figure out what it is that you need, what needs are not being met, and come to him with a list. Then, I would sit down with her. Find out what she needs, why she feels the need to chaperone/supervise your time with him, and explain that your needs are not being met with the way things are now. Last but not least...the three of you need to talk face to face and figure out some type of schedule. Treat it like a custody agreement schedule if you have to. I know you are gone during the week, but when that changes, set a schedule. Google Calendar? It is your friend. Mock schedule. Sunday-Tuesday with her. An overnight visit with you on Wednesday. He can be with her on Thursday and Friday. On Saturday, he can spend the day with her and have date night with you and possibly a night cap. Sunday, the three of you can hang out, grab breakfast/brunch, go to the cinema, go to the park, or do your own things. I do not know your individual schedules, so tweak as needed.
For now, I would still suggest a schedule of sorts. She is with him 7 days a week. She should be able to survive if he spends a night or two with you. The only people I want to be around every day of the week are my children. I can handle not seeing my husband every day. I cannot think of a single person who has something to do every weekend. Even still, perhaps she can attend those things with other relatives or close friends. There is no rule that he says he must attend every single planned thing with her. That is inconsiderate to you, to him, and to your relationship. He might want to do something else, and if he does, perhaps he should be vocal and let her know.
Do you and the chap utilise Skype, FaceTime, Oovoo, or any video chatting interface? I know it is not the same as being right next to someone, but at least you would be able to see him while you are away. People have Skype dates and iSex (instead of iChat) and all of that jazz. If not, why not? Can he not get some time alone to chat with you, ask how your day is going, and just see your face? I would hope she would not want to control that.
