You withdraw your petition, but the other parent can object or counter file. If the parents are not together, there needs to be a court order, even if only mediated, which can be far cheaper to...
This would be different in almost every state. Basically, if the well-being of your children is important, you really should get a lawyer to review the motion and file a response to it. In many areas...
It is always preferable to get legal advise when dealing with any court issues. Most attorneys offer free consultation or charge a minimal fee. If the situation is a amicable one, it's possible...