I've been in the same situation before, and someone once told me not to set myself on fire to keep other people warm.

Do what you can, but not at the expense of your health and sanity. You are not a bad person for keeping an arms length away from your abusers. If anyone says otherwise, tell them they are welcome to tend to said family member instead. Your abusers are not entitled to anything from you, and you have every right to stay safe from them.