If I have full custody (legal and physical) can I keep a sick child back from visitation?

No you must comply with the court orders. You can not unilaterally decide if the child does not go.

No. child support is only retroactive to the date a motion is filed.

What can I do to stop this?

If there is no specific time for you to call the children you should get a specific court order as to exactly when you can call and speak to them....

Yes. He still owes the child support arrears from when you had primary custody. That does not go away. He can now request child support from you...

Can a divorce judgment e reopened if there is an extreme change in circumstances?

The court retains jurisdiction over the issues of child custody and child visitation until the child graduates from high school or turns 19....

You are stuck between a rock and a hard place. If there is no ticket purchased for the child to return home then you can either purchase the ticket...