How do I deal with this difficult situation?

It is very clear what you need to do. It sounds like your brother in law megs needs to spend some more time with his son and his tantrums. You are not wrong at all for disciplining him. "The rod and reproof are what give wisdom; but a boy let on the loose is causing his mother shame." (Proverbs 29:15) I know that you are trying to help because your nephew is your family, but he is old enough to know that he needs to listen to you. If his father is trying to undermine that, then you need to back of f a bit. I'm not saying to write him off completely. You can still invite them both to family functions, but that's it until they both learn how to treat you, and if his father asks why, don't be afraid to tell him the truth.