Sohard,
So sorry to hear about your dog! He’s such a cutie and really does not deserve being the bargaining chip here. And you are doing great coming here to work through the challenge instead of reaching for the bottle.
Your BIL is a jerk, plain and simple. Remember that he probably would love nothing more than to upset you and undermine your relationship with your sister. He is not worth drinking at, but you know that anyway.
Nothing left to do but to accept accept the situation for now and celebrate your newly acquired coping skills. It may not seem this way to you, but you have won an important battle.
Whatever nasty stuff your BIL comes up with in the future, don’t give him the satisfaction of sending you back to alcohol just because he is an evil person. That is his problem, not yours. You are done and that is it. The best revenge is to live well, as they say. Take good care, all my support to you!