I agree with your concerns and it is always best to play it safe. I think it is perfectly right given the situation to ask how long they have been the in recovery. I would have asked and asked other questions. There is a big difference between a few weeks and a few years of recovery. Only you can make the choice of what is safe for your kids. I do not know the history of your story and how you and RHA relate to each other so in no way would I ever suggest a judgment of your actions. You did what you felt was right and that’s good. Parents are protective of there kids and that is normal and healthy.
It does however sound like you are questioning how you reacted to the situation in your post. Maybe he put the question to you the wrong way. If he had told you the grandmother had been sober and in recovery for 10 years – 15 years or something like that would you have been more open to the discussion? Have you ever gone to an open AA meeting with your husband and meet the lady? It may not have changed your mind but the people at AA are close to our significant others and they share a bond and a trust with them. The effort to meet with the person and get the facts about their recovery would give you the information to make an informed decision once you have a better feel for who this person is. At least it would demonstrate to your RAH that you are open to the growth of those going to AA meetings with him and to his growth.
Could your RAH been truly trying to find a helpful solution for you? While his choice may not hve been fully thought through he may have been trying to help.
I would have likely made the same choice as you did.