Hi Wirral,
I have never posted on a thread before but I've felt compelled to post something tonight as in many ways I've been in a very similar position as your daughter.
I think an extremely crucial element to all of this has been the arrival of your ex's girlfriend, and maybe more so, her daughter as well.It's not to say that she doesn't get along with these two, however, it would be very easy for her to be insecure and jealous about her dad playing a fatherly role to another child, particularly when she is an only child.
Although possibly not the main reason your daughter left, her willingness to stay at her dads could be down to her wanting to 'mark her territory' as it were, saying "look dad, i'm here - you can't forget about me now"
Talking about my experience, when my father left us, oddly enough it was not my dad that I was upset with but my mum. I was angry that she wasn't a better wife to be able to keep ahold of my dad. Now, as an adult I know this wasn't the case as it was because my dad went after every bit of skirt going.
But in my irrational, immature head it was my mum at fault, not my dad. I also know that I had unconditional love from my mum, but was unsure if this was the case with my dad, he had rejected us and left after-all!
Your daughter has been through an awful lot: father leaving her, new family unit being introduced, left (what i presume family home) to live with dad, new school, etc etc and to top it all off i bet she's going through puberty aswell!
My only advice is in similar vein to other posters DO NOT WALK AWAY FROM THIS SITUATION as hard as it is to be strong right now, you've got to try your best for you and your daughter's sake. Keep telling her you love her so much, if she allows give her hugs because although she trying to show you how grown up she is, at the end of the day we all need our mammy.
Press for more regular contact, even if it means you and your daughter only meeting up for lunch. Or what about joining a weekly class together. My mum and I used to go to women's only night at our local swimming baths and it was a great bonding experience.
Obviously with this situation things are never going to get sorted out overnight and in the end there may never be a perfect solution. And no you are not an awful or a failure of a mum, if you were, you wouldn't care and wouldn't be posting on a parenting website until the early hours of the morning.