I'm guessing here, but from what I've seen in the past your DD was so excited to have the cat home that she probably pushed it a little bit too far too quickly for that particular cat. I'm also guessing this is your first cat, so neither of you would be able to recognise the rather subtle signals cats can give off when they aren't happy with something.
This isn't in any way to blame your daughter, she's acting the same as any child of that age (especially a girl) would do and just wanted to make friends. If the cat was a bit offish your DD probably tried harder to make friends, until eventually the cat took a swipe. Now you have the cycle of DD trying to make friends, cat trying to keep her away, so DD tries harder.
IF - and that's a big if - you feel it could be worth another go, have a chat with the rescue. Say you think this may have happened and you will try from the start, if they would be happy to extend the trial period.
This will involve your DD having to near enough ignore the cat for some time now, we're talking maybe weeks rather than a few days. Same goes for you. She gets fed, watered, litter done, spoken to (softly) like you would a frightened child. Left to go where she's comfortable, when she's comfortable with absolutely no interference. In time, she will start to come out more and enjoy your company.
In the interim, read up a bit on cat behaviour and the signals the put out. Have a poke round a few videos of Jackson Galaxy on YouYube, or see if you can watch his "Cat from Hell" series (hint - most of the cats had issues that he sorts).