I'm going to ruin my nephew's birthday party after I was mocked and made fun of by my family
How do you plan to ruin your nephew's party?
I'm going to refuse to let him play video games all by himself and I'll ignore his teary eyes.
It seems that you are taking out your anger on your nephew because he is the easiest target and that is wrong. Instead, you should tell your family how you feel about their actions. It would be unfair to punish your nephew for something outside of his control and this could lead to further problems with your family.
I just need to vent.
Don't use your nephew to vent. It wasn't him that made fun of you.