I'm sure you've had a rough time these past couple years, and my heart goes out to you. However, your daughter is acting out because that's the only way she can communicate the trauma that's going on inside her. You may be ready to date others and replace your ex-husband, but from her viewpoint, she is NOT ready to replace her daddy.
Most reputable child psychologists will tell you to not have your daughter involved at all with anyone you date, unless it's serious enough that you're planning to marry that person. (no matter the age of the child) I'm sure it gets lonely without adult companionship, but if you're going to date, do it during times when your daughter is with her dad, or another trusted caregiver. Or maybe trade childcare with a neighbor so it's not expensive. If he doesn't understand this, then dump him now. I also recommend the book by Dr. Laura. I know it's tough on you, but I agree with the others that your daughter must come first. Hang in there.