You don't say if the parties are married, if there is a parenting plan in place or anything else that would define what rights the father has. If there is no parenting plan and the parties were never married, the father has not established his legal right to see the children and the mother has no obligation to send them. If there is a parenting plan and the father has not seen them in three years, the mother can get an emergency order to prevent him from seeing the kids until he has met certain conditions (e.g. seen them in a supervised situation for a period of time until they actually get to know him after all this time). If the parties are still married, it's time to file for a divorce and again, she can get an emergency order. No court will require her to put 4 year olds on a plane to see someone they have seen once in the last three years. But she can't just sit on her thumbs. She needs to get the kids legal situation straightened out vis a vis the father. Child support has nothing to do with it.
Answered on Dec 15th, 2014 at 6:07 PM