Hi. the French word "abuser" does not mean to abuse . They are false friends. It means : "to do something too much" (abuser without a complement), or "to eat or drink too much of something" (abuser de quelque chose).
I would say "violent" in your case.
actually you could say "parent abusif", but this would be understood as an exaggerating parent, i.e. someone that exaggerates their use of violence, or abuse on their children. Somewhat far fetched, I think.