I too, have a six year old who enjoys touching himself. Although he is not so private about it. I have commented on him to stop it. He will just stick his hands down his pants while watching TV. He also rubs his penis on things like furniture and stuff. His pants are up of course. I feel this type of behavior is normal in children of this age group. If is a form of self discovery. A concern of mine is, if you have custody of your daughter and allow her to stay with her mother, however nice of you, after finding out information like you did, why did you continue to allow her to stay there? If it were me and my child made comments to apparent sexual behavior in front of the children, I would want them with me until the situation could and should be addressed. There is no law that prohibits a man and a woman from sleeping naked together, but discretion is always neccessary when children are involved. Their little minds are so impressionable.
Masturbation is normal! Please do not even think of punishing her for this. I agree with Rock Rose that she needs to know where it is private (such as alone in her bed, in the bathroom, etc) not in front of others. Talk with mom re issues wiht boyfriend. If you get no where, just tell your daughter that grownups sometimes do this when they are in love, to show their love. There are many things that are ok for adults that are not ok for children.
There is a great sex ed book out...Where did I come from...Peter Mayle I think is the author. It explains many things, such as masturbation. It does sort of tickle doesnt it?
I don't understand why parents ask why children do this. Why does anyone masturbate? Because it feels good!
The problem here, is although you say she's doing it in "private", apparently she isn't if everyone knows about it.
She needs to learn to do things "privately".
Also, that is TOTALLY inappropriate that a 6 year old little girl is aware that her mother and some man are sleeping naked. Talk about not understanding how to keep things private!! Before you think about having "the talk" with your little girl, try to rattle some sense into her dumb mother.