NP -I'm sorry you are in a most difficult family situation.

I think the only way it will get better for you and your relationship with your therapist is to remove yourself physically from the violence in the home. I am pretty sure your therapist has told you this if you are being open with him as you are in this post. I certainly understand any therapist reluctance to receive these emails on a daily bases whether he reads them or not. And, I am not one to cut a therapist any slack when it comes to the amount of emails a client sends. In some US states he is obligated to report physical domestic abuse. Until you are physically safe it doesn't matter how many times you see your therapist or don't see him — you are in serious danger. If you have children they are in harms way. I urge you to contact a domestic violence organization and get the hell out!

If you stay in your family situation then I think what your therapist has offered you is a good deal in comparison to other email take-aways that other posters have had to deal with. But, I truly hope you find an immediate way out.