What happens if I don’t send my children to a court ordered visitation out of state since he has been in jail at least 3 times in the last 6 months?

You can be held in contempt. What do you mean "has to drop for drugs?" If he is using heroine now and you have actual evidence, then go to court on a motion to suspend visitation until he cleans up. His criminal convictions are not violent crimes and will therefore not make a huge amount of difference in whether he gets time with the kids or not.

Your children's father could file a motion for contempt for your failure to abide by the court's order, but in your case, I believe it is justified. That being said, you should immediately file a motion to suspend his visitation and perhaps even a petition for modification to get the order changed. You have to take immediate steps to protect your children if you feel like they are in danger. It sounds as if they could very well be if you allow them to visit with the father.

It would be my suggestion you file an application to modify the decree, terminating the parenting time, setting forth the reasons you have listed.

There are a few likely consequences. The most likely negative consequence would be if your ex petitions the court to enforce his rights to custody. You would then have to go to court and explain why you did not follow the court's order regarding custody. While this could result in you being held in contempt (likely necessitating fines or possibly minimal jail time) it sounds like your excuses could prevent this from happening. I would recommend contacting an experienced attorney and bringing an action to change the current custodial arrangement. It sounds like you have a very strong case that it is not in the best interests of the children to be spending time with your ex.

You are in contempt of court. Get the order changed. He was an addict and probably a thief when you divorced him. Jail appears to be the only thing that changed, except your willingness to send the child to him.

You could be found in contempt of court if he files a motion. You will need to show the court that your behavior was reasonable.