Oh come on Blossom, you can't say you've rushed nothing after your own OP said you went at a "hundred miles an hour" 
Even if it was him pushing it, you went along with it.
You knew him 'a few months' which sounds like 3? So 7 months after the child got a new 'stepdad' in her home and had to process her mum's affair. Now you say she was being used as a weapon by her mother - even more reason that you and her father should have kept your relationship away from her for now.
Her mother's behaviour does not sound ideal. Although her XH isn't sounding great here, so I'm beginning to have sympathy for her leaving him! But not for an affair, and not for making her daughter live with him so quickly.
But look - I think you're now displacing who is in the wrong from the 'manipulative' daughter to the 'bad' mother.
The person who has pissed his daughter about here, and you too, is HIM.
So the daughter said "yeah she's OK but I want you to myself?". That's not manipulation! She went from having her dad full time to weekends only, and after what 7-8 months she's now sharing the weekends? I don't think it's manipulative for her to say she's unhappy.
I'm sorry you're hurt by his behaviour but you need to stop blaming the mother and daughter and blame HIM. He wanted the whirlwind romance, pushed it, now it's slightly hard because he has to deal with his daughter's feelings do he's thrown in the towel.
Live and learn, move on.