Can you have a child removed for immoral character?

I'm not sure how to put it, but I'll briefly explain the situation: I have a 7 year old daughter who is in the primary custody of her mother, while I have visitation. What is really bothering me is that over the past three years, this woman has had no fewer that five (FIVE!) different men living with them while it seems like just about every month or so you will her walking and holding hands with some guy, and you'll shake your head and say "Okay, and now who is THAT?" Personally, I think it's a desperate quest to "catch up" with me since this all started after I met someone I truly felt a connection with and married her--but that is just a guess, and it really doesn't matter.

What matters is that we have a 7 year old girl who is seeing man after man after man coming through her life which is not only confusing and damaging her emotionally, but she is also going to grow to believe that it's perfectly normal change men like you change your contact lenses! Could I use this to petition for full custody until this woman decides exactly what it is that she truly wants? This is not healthy for a child in the least bit!

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