This seems fixable to me. Here's what's at stake. If you leave him, and go on to date other men, it's highly unlikely they will treat your daughter well. It's likely the man you replace your boyfriend with will have children of his own, and favor them, and you'll favor yours, and then you'll have another child with him and be stuck and your daughter will have a childhood of being rejected. Your boyfriend will go on to have other children, and your daughter will be a guest in his home and not wanted by the new girlfriend. That's truly what's MOST likely to happen if you leave.
I agree with Nighthawk that the brothers should probably leave. That's too many people in a two bedroom apartment. Are they planning to be permanent? Are they minors?
Do you have friends? This is a time in your life where it is extremely easy to form friendships with other groups of young mothers, and you could form a very strong social network of moms who like to do really fun stuff, mostly with but sometimes without the kids. I have friends who mostly socialize with other women, because their husbands prefer to stay at home, and it works out.
I recommend "the proper care and feeding of marriage" by Dr. Laura Schlessinger. Some good tips in there. Best wishes.
It might also help you to do some sort of volunteer work, maybe in a food bank, soup kitchen, abused women's shelter etc. If you do decide to go to college and work, it employers will be looking to see that you are socialized yourself in a professional setting (not just college), A part time job would also work. You've mentioned that he's a good dad, maybe he wouldn't mind looking after the little one so that you can start to build a resume.
This may also be a case of you needing to start to get back to school, so that you can go to work when the baby is on their way to school. I don't know if you've finished your GED yet, but if not, i suggest that you get that out of the way so that you're ready to go to college. This might be a case of you needing a fulfilling career of your own, where you can have interaction with other adults on a daily basis.
I think your house guests should probably find their own place. I don't think your relationship is strong enough to withstand the lack of privacy or intimacy. You're depressed, and i think it would help for you to talk to a therapist and talk about how you feel. See what input you get. Third, I think you need to go to marriage counseling. I think you need to know that he's as committed as you are in finding your happiness. I think you need to do all you can to try to revive your marriage, and it might help him to know how important it is for you to keep the family together, if it can be saved. Then, if you do decide the best thing to do is a formal separation and divorce, you know you can tell your child that you did everything you could to stay together and you'll know you did everything you could. When i met my now husband, he was recently separated from his wife (not yet divorced).. I called his wife and asked her if she had any thoughts about reconciliation, or counseling, whether she was done with him or not. I told her to please think about it and let me know. She told me there and then, that it was over for her, that i could have him. Had i not made the move of contacting her, i think i would probably be feeling guilty to this day. They had an 11 year old daughter at the time of their separating so it was really important for me to be able to sleep at night. You can't let this go, you need to talk about it all and find resolution. Your depression will not cease until you do, and it may get worse . Please seek therapeutic help. You're worth it. Hopefully you can afford to make these moves, you mentioned that he's a good provider so hopefully you can budget for your mental health and to see if a counselor can get you two to make some changes together.
You've mentioned that you like to socialize, so do you do anything social without your husband? do you go out with friends for instance ? If you haven't already done so, why not consider joining a gym where you can attend some classes? The exercise will help your mood, and making more friends to socialize with will help your need to get out with others. Join a walking group that you can also take your child. Maybe join a mommy group. Also, do you normally work, or are you working now? If you're a stay at home mom and in need of more socializing, and you husband works full time (maybe even more than full time) he may be too tired when he gets home to go out and socialize with others. Maybe he's had so much of people other than his family, he just wants to spend his free time with family. If he's a great dad and a great provider, allowing you to be able to stay home with your child, it might be you that also needs to compromise and accept that maybe he's just too tired and not interested in meeting any more people than he already has to deal with at work?
I'm glad you posted and hope that something i said maybe has helped. If you want to talk more, please send me a private message, i'd love to talk to your further. Please let us know what you decide to do moving forward.