I'm not going to my dad's to hang out with my cousin
Are you trying to avoid him or something?
Yes, I had a fight with him earlier.
Well, I'm sorry that happened.  I think it's fine to avoid a family member that you don't want to hang out with, especially when it's after you had a fight.  I hope you patch things up in the long run!
No, I'm going to make a big deal out of it.
If I were you, I would try to just let it go. It is not cool to hold grudges against your family members.