Changing schools so many times is not a good thing, in my opinion. Many young adults, and adults as a matter of fact, have an extreme fear of change and once they are faced with change it cannot always be a good thing.
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You have a lot to consider. Each time your daughter changes academic settings - she has to readjust . New schools mean, new friends, new teachers, new expectations! It is important to recognize and be sensitive to your daughter's dilemma.
Additionally, it sounds as if there are some major financial considerations on the table. I think you really need to first evaluate if private school is something you are going to be able to support and pay for. If not, then you will have to move her again. If that is the case, then you need to make a plan to move her.
In order to make the move a positive change, you will have to prepare her. It is important that you address the things at the private school which are a problem. Just because you are removing her - does not mean you are avoiding and running away from problems. I think you should take on those issues with her - and help work through those feelings.
I think it would be wise to address the change - for honest reasons. If it is a matter of economics - explain that you have decided that there was not cost justification to continue to pay to be in an environment which was not suited to her needs.
It is important to stress the value of a good education. It would appear that the Charter school was the original first choice, and now that there is an opening that you will be taking advantage of that opportunity. You will need to keep her supported through this transition. Moving is really tough on kids, especially in Middle School. I think once you make a decision, and make a plan you will feel more comfortable.
Best of Luck!