Brooke:
Ditto with everyone else: you are in the right here. Your ex sounds incredibly immature. His daughter is a human being, not a puppy to show off when he wants and pass off to someone else when inconvenient. Heck, even puppies need to form healthy attachments and shouldn't be passed around from person to person based on a whim.
However, if it's not stipulated in your parenting plan and he has visitation rights, he can introduce her to whomever he wants when she's with him.
I would go back to your lawyer and talk about how to get this in writing. If that is not possible and your ex has visitation rights, you're going to have to continue to appeal to his conscience.
Perhaps you've already done this, but if not, you could try writing him a letter that expresses your concerns along with your memories of growing up with a lot of your mom's boyfriends.
Try to state the good things you remember about him; mention the areas in your marriage that YOU are sorry for. In other words, try to show him that you are not just bitter and angry about everything, which would make him believe you are just trying to seek revenge. I would also let him know that you fully understand and expect that he (and you) will have other relationships and that your daughter will meet some of these people during her life. Wish him well in his current relationship.
Then tell him when you would be comfortable with either of you introducing a new person in her life - be sure to tell him that you will agree to everything you are asking from him. If he has to be in a relationship for at least 6 months, so do you.
Have a neutral person read the letter and don't be defensive if they say your letter sounds too angry or bitter. It's really, really hard for us to hear or see ourselves objectively.
I wish you the best of luck with this - people do change and it's absolutely possible your ex will mature over time and become a wonderful daddy to his daughter. At this point, however, he is only thinking about himself. I have prayed for you and your daughter and I hope things work out for the best.