I completely understand. He is a creep to have done this to your family. Such a selfish act.
I promise, no one can take your place as your daughters mother. She will always love you with all of her heart. Remember she will also always love her father just as much. Even with all of his flaws.
As long as this woman is good to your daughter, if would let it be. I do not think sleepovers will affect your daughter and HER self worth. My father had many girl friends and it did not make me and my sister fast and easy with our morals or feel anything except pity for my father being so ridiculous.
Remember at some point you may meet someone and want a sleepover.
I was a child of divorce and the one thing I hated was the fighting my parents would have AFTER their divorce. Yes, I knew their was tension.. I heard the phone calls was witness to their conversations. Saw my mother cry, heard my father yell about his girlfriends to my mom.. .
I will never forgive them for this. They are the adults and yes, they were not directing any of this at me, but they are each a part of me so when one said something about the other, it hurt my feelings because I loved them equally.
Their divorce was THEIRS. Yes, my dad was the main reason for the divorce, but I should not have been made to have such torn feelings about my family.
Please try to protect your daughter from the negativity. It is hard enough to leave you and then just as hard for her to leave dad! No matter what she says to you.. She will protect your feelings.. it takes lots of energy for your daughter to do this.
Find a therapist and talk out all of your feelings. You have a right to be furious, hurt and disgusted, but you now also deserve to find happiness and not carry all of this around alone. Your feelings are real, you need to be heard.
Hang in there, I am sending you peace and strength.