M., Good for you for taking steps to improve your life and the life you can give your daughter! Being a full time parent, bread winner, and taking advanced classes is a full plate!It's so easy to become emoitally and physically exhausted in situations like this. Make sure you take time to be alone and rest! I've been there and I feel for you!
Your daughter sounds like a 5 year old! At this age, children will start to show their independance and individuality in ways you haven't seen before. That's o.k., but she needs to learn that it is never o.k. to be rude or hurtful. What worked for my daughters was telling them what needed to happen, then giving them a choice. "It's time to get ready for bed. Do you want to brush your teeth first, or brush your hair first?" "We need to get dressed now. Do you want to wear the blue dress or the yellow one?" Then do it in her chosen order. Don't give her choices that are not an option. Safety issues are NEVER negotiable. Try something like "You must sit down and keep your seat belt on in the car. I love you and want to keep you safe."
It's hard, but do not be too hurt by her statement that she wants to live with Dad. It happens with most children whose parents do not live together and it is often part of them trying to see where they fit into the situation. If you go into hysterics about statements like that, she'll use them to control your behavior and you don't want a five year old controlling your adult life! It doesn't make her a bad child-she's just learning about her environment. A frank discussion at her level of understanding is important and you might have to have it several times- something that reaffirms her love for you and her Dad and both of your love for her. Let her know that saying things like that when she's mad hurts your feelings.
She also needs to know that Mom needs time with her adult friends. You didn't say how long you've been dating this man or how serious you two are-Be careful about how soon you introduce a new man into her life. She still loves Dad and doesn't understand that this new guy isn't going to take his place in her life. Talking about this isn't going to change her mind either. Time and his behavior will help her understand this. As far as her wanting to be the center of attention when he's arround, she's five and this is normal-here is a new person to give her attention.
Best wishes, M.. Mothers and daughters have a unique relationship and when it's only the two of you, it is often strained when a new person or situation is introduced. What ever happens, make sure she knows you still love her, take care of yourself, and you will find your way through this!