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Yes In most of the United States (though not everywhere), school districting is geographically based. Your children are assigned to a school based on their home residence address. So yes, the schools are obligated to take your children, as long as they are of the right age.
Furthermore, it sounds like you are relocating prior to the start of the school year. So it's no problem for you to register your children in time for the new school year. Or should I say your child...
Your 3 year-old is still too young for most public school programs. You will likely need to find a private pre-K, though there are a few public pre-k programs. But your 6 year-old would likely be eligible to register for first grade.
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