I'm not going to invite my mum's new partner to a family event my dad will be at
Why don't you want to invite him your family event?
Because I don't want any drama between my dad and my mom, their divorce was terrible enough.
I can understand your apprehension, but I still think it is rude to deny invitation to your parent's new significant other. Let your mother make the decision on who to invite, she is more involved in the situation.
I do not want them to start fighting.
Let her decide who can go and who cannot go, it is better that way.