As far as "permission" goes, broken bones is definitely beyond requiring your permission. Hospitals are required to ask and report if the answer is "my dad broke my rib".

You are knee deep in a co-dependent relationship, which has you defending your abusers. I know it is tough now, but this is better for you in the long run. They have to take some responsibility for their actions. That won't happen if their actions are always "excusable".