Does the daughter live with her father? If she doesn't then why are you, after such a short time of only 10 months, honing in on her father/daughter time with her dad? Can't you see your bf (her father) when it's not her time to visit until she's had a chance to get used to her father with a new woman?
If she does live with him then you're just going to have to be more patient (it's only been 10 months) and if he doesn't tell her to quit the rudeness then you're going to have to have talk with him about how disrespected you feel when she is rude to you. I know my husband won't tolerate it if our daughter is disrespectful to me and vice versa. He should know that his daughter's ill behaviour is not acceptable to begin with.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion