She is overly affectionate to everyone she meets -- kissing, hugging, licking, and crawling onto the laps of anyone within reach. She is not a small child anymore and her behavior makes me uncomfortable. She is an extremely bright, funny, and sweet girl, but something seems bizarre to me.
I'm surprised her mom doesn't provide her with a bed of her own to sleep in when she is staying with her, rather than setting up a situation where mother and daughter have to sleep snuggling one another. Being overly affectionate with everyone she meets is clearly inappropriate social behavior for a girl approaching nine years old. Her making kissing sounds over the phone to her mom as she tells her she can't wait to snuggle (in bed) with her is also an abnormal, sexualized discussion between mother and daughter.
She may be going through the early stages of puberty and experiencing sexual feelings that she wants to act upon in these affectionate ways. But what troubles me is the obsessive, incessant, and sexualized behavior both with the adults she knows and with strangers.
I am also concerned by her mother's apparent encouragement of these sexualized behaviors. Some experts might suggest that your stepdaughter has been acting out in this sexualized manner because she may have suffered sexual abuse of some kind. I don't wish to alarm you with this observation, but I would strongly suggest that you and your husband consult with a child therapist who has dealt with children who have manifested these types of overly affectionate, sexualized behaviors.
Do not take her to a therapist before you have had consultations on your own. It would be very helpful if her mom would participate, but I suspect there might be resistance there. Ask for her help, in any event. I don't think these are behaviors that should merely be allowed to continue. There are too many of them occurring on a continuing basis and their origins and obsessive nature need to be explored with a professional.