He can demand all he wants, you are under zero obligation to provide.
The current court orders stand as they are until someone files to change them and the court orders a change.
If he wants long distance visitation, let him file for it. Till then, you are bound by your current court orders.If I were you, I would keep some sort of log with when he actually shows up for his visitation and when he doesn't. Down the road, you don't want him hauling you to court because he failed to exercise his visitation and he blames you.
Unless you were ordered to transport the children to him in the current court orders, you do not have to do that. If, for some reason, you were court ordered to transport the children to him, then you would still have to. In that case, it would be prudent for you to file for the modfication to a long distance plan and request he be responsible for all transportation to and from your home for his time with the children and all costs associated with the transportation, particularly since he isn't paying child support.
Child support and visitation are not tied together...you need to file for contempt or a show cause in regards to the child support. Something tells me if you do that, he will not be very likely to file himself for the visitation change.
Best guidance...don't listen to your ex about what YOU have to do because that's how he wants it. He isn't a lawyer and there is no court order requiring you to do so.