Raising Step Children

So I have been with my guy for just over three years; his daughter is now7 and suffers from many psychological problems. Her Mother has never allowed her to sleep by herself; she has never experienced her own room. She has also been the recipient of always winning games from her peers and role models alike. Now that me and my boyfriend have our own place, she stays with us for 2 to 3 days a week. Don't get me wrong, I love her dearly, and I think that this is why we are having problems. I have been telling my guy that he should get his daughter into counseling ASAP, mostly because of the lack of stability and uniformity between him and his ex. Not to mention the different cultures (she (Mom) is Korean and Dad is pure white American. Her (daughter) lying has become more and more predominant and today she stole $120 out of my purse...at seven years old! He (my boyfriend) did not tell me until after he dropped his daughter off with her Mom; and of course I became upset and actually refrained from the old I told you so type of response. Well, his confession and my reaction have led to one of the worst arguments in which we have ever had. He walked off (of course), and I am here feeling very hurt, confused, and angry! I did not yell nor even raise my voice! I hate this feeling and my first instinct is always to run, move out, or whatever! ARRRRGHHHH!!!!!!!