It’s called alienation and it’s abuse. Your ex-partner is teaching your children that it is ok to belittle you to your face.
The next time your teens do it, bring them up sharp. Make it clear it is not acceptable and they are bullying you. Bullies don’t get to use broadband. Turn the router off until they treat you politely. And stick with it.
Record details of each comment and then send an email to your ex saying that if this pattern continues, you will consult a solicitor. It is not ok.