I'd really like to be her friend but she has trust issues?

I've known her for a few years now through her boyfriend, my ex and a few of our mutual friends. I have been living in her house with she, my friend *her guy* and her daughter. I nvite her to stuff *job hunts, BBQ's* all the time and she accepts but is really standoffish. Complains a good amount and doesn't attempt to "bond" with my other friends. The other day I overheard her say that she hasn't found any friends "worthy" enough to hang with. This kinda hurt my feelings. She considers this lady who isn't really all that stable a closer friend than those who have themselves together. Where I come from, people share and smile A LOT and have a Southern Hospitality. My bf says that she may think I do a lot of "extra" stuff and she may see it as unneccessary. Its just my character! She doesn't trust her guy *my friend* and has openly admit this to me. Should I not invite her to stuff anymore or even try to hang out w/her?