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So long as you have the original court order and proof that your daughter has lived with you and attended school there where you live, there should be no issues when you return to pick her up for the start of this upcoming school year. You can even ask the police to assist you if your ex wants to try to refuse returning her to you. Regarding whether or not she can alternate her school years between the two of you, that does sound very disruptive and if your ex seriously wants to do that she will have to petition in the court where the original decree was entered into (AZ) seeking to change the current arrangements - and then the judge must perform an analysis of what is in the "best interests" of your child -- the court will consider what she wants because she is a teenager but the court will not automatically do what she wants -- that factor will be looked on along with all other factors regarding whether the split year school arrangement is in the best interests of your child -- the other factors are how long she has been going to school where you live, her family and school & religious ties there, if there are other issues in either your home or your ex's home that the judge might want to hear to make a decision and basically the judge can use any other criteria that he/she wants to use to determine what is in the best interests of your child in this case.
Under the circumstances you describe, I have a hard time believing that a judge will go for the "split year" arrangements if your ex does try to bring this forth in the courts.
Yes it does make a difference and I apologize for the discrepancy (I answered a question about a teenager in a similar situation about 2 minutes before I answered your question).
The difference is that the court will not seek your daughter's input here on where she wants to live because 6 years old is too young to make that decision. The court will do the same "best interests" of the child test that I described above except without your daughter's input -- so that will more than likely favor your situation if your 6 year old actually wants to do this with the alternating school years -- because the judge will likely find that at her age it is simply not stable enough for her to try something like this.