OK, well I am going to assume that by moving in with each other your relationship has gotten very serious and you are not simply "casually dating as some posters here may assume. LOL! I am going to give you some background here. First of all, I am a mother of 4 beautiful kids, ages 7 yrs to 20 yrs old. My oldest recently came to my husband and I, well at least her boyfriend did and asked if he could propose to her in the near future. He is talking about in the next 6 months or so. We love him, and he is family already as they have been together for quite some time. They are very "young" though, and we told him that 1 of the several conditions that we would have prior to getting MARRIED, (not engaged) would be for them to actually live together for at least a year, without breaking up. Look, marriges seem to be pretty disposable these days, and my hubby and I are coming up on our 21st annev this month, which makes 24 yrs together. Yes, we were 18 when I met him, but I was a much "older" 18 than my daughter. Not quite so sheltered and young since I had already lived on my own and gone to college for a while. My point is, you don't really know someone until you live with them full time. You need to share expenses, the duties of a home and kids if you have them, see how you react to stress, and frankly, see how the other will react when you are sick. Can this person take care of you if you are down with the flu? Sounds weird, but those things are very important. It's much easier to wak away from something BEFORE you are legally married.
Now as far as the kids go, they will be fine. How do they get along with you all now? Your daughter is very young. Does she like your boyfriend? Is there contact with the bio Dad? If not, you are doing her a big favor potentially by allowing her to have a stable and healthy man in her life who is willing to act as a role model for her. Don't worry about who is doing the discipline with her unless you do not agree on how it should be done. Bottom line, she is YOUR child, so you do get final say. I believe that you really should take his ideas into consideration if you live together, unless he is pushing for some type of corporal punishment that you do not believe in, which in that case I doubt that you would be with him if that was the case. Your child needs to know that the 2 of you are a UNITED front when it comes to her rules and will stand together on all decisions. His kds should be the same, however since they will be there less, he should be the one who actually speaks to them about any behavior issues. You should have input in the decisions, and they should know that you are together on them as always, but let him do the actual doling out of any necesary punishments for a while, at least until you are all more comfortable with each other. Let all of the kids know that this is THEIR house together with you both, and nobody gets left out, no matter how much or little time that they spend there. Your daughter cannot end up the "queen bee" just because she lives there full time, however, she does get to have certain things that are hers and hers alone because lets face it, they have a home to go to that she does not. They are old enough to explain it to and just that way. I am sure she will be so happy to see tham and to be able to "hang out" with them for a little while when they do come visit, that she won't really care what they touch of hers or what they do. Mixed fmilies manage all of the time, and do so very successfully. It can be a lot of work, but it is very rewarding too. I bet in a few months you will look back and wonder why you were so nervous about this all after all. LOL! Good luck!