EA, PA, schmEA...an inappropriate relationship is an inappropriate relationship. Since you're "separated" then she has to respect the same boundaries any roommate would, with the added complication of being your child's caretaker.
If you don't want him in your living space or around your daughter then state that. If she crosses your boundary research your options.
You don't want conflict to escalate but make sure you are protecting your daughter and your interests. It is inappropriate for the mother of your child to be introducing an adult male figure in your child's life during this time of flux. You may need to go to counselling together for your child so that she hears that from an impartial party but get it done ASAP.
