I think the OP has kind of made her bed and has to lie in it I'm afraid as there isn't a magic wand she can wave to make it better. Seeing as moving back isn't an option, but all isn't lost as things may come right in the end.
The thing is she was uprooted just at the age where the influence and significance of parents is transferring to the peer group. If she was settled and thriving socially it's a shame that had to be obliterated. Particularly for a young girl as wider society has this annoying and pernicious habit of knocking the crap out of girl's self esteem. Iirc a report last year concluded that this gap starts to be measurable from the age of 6.
I know this sounds harsh, and I'm only being so hard on behalf of other parents considering moves at a similar time in the children's lives. I'm not saying never ever move, but children aren't considered enough in situations like this. The thing is the parent-child relationship is the only major relationship that is involuntary (from the perspective of the child obvs!), and thus parents have to hold themselves accountable to a higher standard of behaviour than a friend/partner as the option leave exists.
My guiding star once my child is old enough to be an adult would they look back and reflect and feel they couldn't have chosen a better parent? I find this question helps in examining questions of this nature.
To the OP you are in damage control mode I'm not sure how long there was between the relationship breakdown and the move? If it was short she has had a tremendous amount of change to process and the loss of an old life to grieve for. As children we crave the safety and security our parents provide and when a parent is responsible for diminishing that it damages the credibility of that parent, like I said couldn't be a worse time as her peer group were starting to usurp your parental influence.
What I'd zero in on with your daughter is her self esteem, my guess is she is feeling like a failure, and because she loves you she doesn't want to undermine the happiness you have acquired post move. I'd be inclined to approach her honestly and reflect that you feel like you made the wrong decision, and you would never have countenanced the move if you had realised the impact this would have had, and ask her to unpack her feelings even if that means she expresses emotional negativity about and towards you, take it on the chin and start working on what she needs to do to rebuild herself.
Fwiw I don't think you are a bad mother as I suspect you were in the position of having to choose the least worse option here, as it's clear you love your daughter deeply as she does you. As hard as this post may be to read (and if I'm way off base just ignore it as Internet ramblings!), put a pin in the guilt you are feeling as I suspect it is contributing to an emotional/communication blockage with your daughter. Best of luck and I hope it works out.