S.E.
Your daughter's response to your boyfriend is completely normal. It appears that your relationship with him has gotten much more serious, and that threatens her in a couple of ways: 1) she is no longer the primary focus of your life; and 2) she really likes him, and is afraid that he'll leave too, just like her dad did.
For the first, you need to spend separate alone time with your daughter, that has nothing to do with your boyfriend. Until he's your husband, what's he doing over every single night? You might not be able to change that and go backwards, but you do need to have special "mommy and me" time with her, when he is not around at all.
For the second issue, he's a grown man, and all he needs to do is continue to reassure her that he likes her. If he has trouble not reacting to her distress, then you need a few sessions of family therapy to work on this. Your daughter doesn't need therapy by herself, that will only reinforce that she's the odd man out here and not really part of this family. If you're serious about making the three of you into a family, you'll need to do some repair work first with her, and then with the three of you as a unit. If he's not that committed to go through this kind of emotional process, then he's not ready for a real relationship. That will be a great lesson for the next time - go slow when you're a single mother, because everything you do has huge ramifications for your child.
Good luck!