Meadow was smart enough to know what Tony was involved in, but I think that like any daughter,she didn't believe that he was capable of murders,and extreme violence.
I think she convinced herself that his main business was gambling,even though at some point she had a harder time maintaining that self delusion. Also ,In as much as she was supposedly disgusted with Tony's way of making a living,she would not be beyond taking advantage of it to her benefit. I could almost guarantee that she knew what the effect of dropping the Soprano name would have on someone she might be seeking a favor from.