13 is a very tricky age .Only 18 months ago she lived with both parents, now she's in the midst of puberty and being shunted between two homes and parents at war. Now her father "has a girlfriend".
Think what that means to a 13 yr old. How she sees it.
"My mum is not how and who she used to be. People can change.
Dad has stopped loving MUM. So now I know my Dad can change his mind about who he loves.
Dad has left Mum, me and our home . So now I know Dad might leave anyone he loves
Dad has found a woman he likes better than the old one (Mum) and now she's getting all his attention and love and they are having sex and maybe he'll have a new baby he loves better than the old one (me) and I'll get left, ( like Mum)."
She has totally lost control of everything; her family, her home life as it was before. She is absolutely terrified of losing Dad , of being abandoned, or rejected , or replaced, because that all happened to her Mum
Refusing to meet you is the ONLY THING that's within her power, the ONLY WAY she can have a say , the ONLY WAY she can make Dad listen , her only hope of splitting you up, and she's doing it.
It's far, far too soon to expect her to accept you.