I'm the child of divorce and my mother was a serial dater. It was not pleasant. We felt we did not come first (sis and I). We HAD to go to our dad's on the weekend so she could have "her" time. I know you're not thinking the same way, but this is what kids can pick up sometimes.
It's too soon to involve him in her life as your boyfriend. She's not ready. And she may be used to the vibe at daddy's, but she has to share daddy with the "new" family, and now she's going to have to "share" mommy. Of course she's jealous. She feels like she might lose your attention as well. You can't make her be OK or act "normal". The situation isn't normal.
Dating with kids is so different than just dating. Every relationship you have now involves 3 people, you/daughter and the guy. The guys have to know this going in.
If you just want to have fun and not get married, then don't introduce the guys AT ALL. Emotional pain all around if you do. If you DO want to get married, wait till you're both feeling serious before starting the "family bonding" track. It sucks to like the boyfriend, and then go through the breakup, because the adult is NOT the only person breaking up with the man, the kid goes through it too. It's hard.
If he's a keeper, and you want to keep him, he'll understand, especially if he's a friend of the family. If he's selfish about it, cut him loose.
Good luck!