If the word of your ex was the only evidence and that has been shown to be untrue, then you should be able to obtain the retunr of your children. This assumes there are no other factors present in your case. You should have an attorney to press the issue in court and protect your rights.
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Yes, it is possible, but you should speak to an attorney in your area to assist you and lead you on the right path. Many attorneys offer free consulations so call one ASAP.
It is certainly an issue that should be brought up at the next court appearance. If you have an attorney, discuss your concerns with him/her, and if you do not, retain an attorney to better explain your situation to the Court.