This situation is more complex than a traditional request for child support modification case. I strongly suggest that you retain an attorney to assist you.
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If you are asking whether you can move, yes you can. Will your child support be reduced due to your move - it may or may not. More information would be needed to give you a more detailed answer. You should consult with an experienced attorney. This is not an easy question to answer online.
This answer is being made for informational purposes only. It does not constitute legal advice. By responding to a question, no attorney-client relationship has been established.
Your child support obligation will not change because you choose to move to Europe. If you voluntarily take a job that pays less, the court may order that your child support obligation continue without a decrease.