I used to run a railway station and we regularly had youngsters travelling who were much younger than 13. (There is definitely no legal minimum age)
If you travelled by train in the South East of England, you'd see plenty of 8 year olds who travel on their own to and from independent schools, by train, every day.
My friend's son regularly travelled between his parent's home and his uncle's house. He was on his own from the moment he got into a taxi in Sheffield until he got out of one in Paris. He was perfectly sensible and responsible and there was never any concern for his safety.
Thirteen year olds need their independence. Parents have a duty to help them achieve it. It's about time that your ex-husband realised that there are only two-and-a-bit years before your son will be able to leave home, get married (with parental consent) and start raising his own family.
I'm not sure, however, what a court would say about the situation. Your best approach might be to try to force him to do his 50% of the travelling. Faced with that, he might suddenly decide that the boys are old enough to travel on their own.
Chris