HFA,
Congratulations on your 15 days sober. Way to go. Sounds like your getting your life together. A new start for you.
Divorce is always hard on children. The only advice I can give is make sure you spend some alone time with your daughter. Its very important to make her feel special and that your love for her remains consistent no matter the changes taking place.
As far as new girlfriend , this will take a bit of time. Daughter may feel threatend and her loyalty is with her Mother. She may feel she's betraying her Mom by liking your new girlfriend. She's just confused right now. It's up to you Dad to calm her fears.
Stay strong and have patience. Change is harder for some then others.