Please try and put this into sober perspective and at day 6 this might be difficult, because your mind will try and give you reason to drink again. Your BF and his ex have children, there will be contact between them, there has to be for the sake of the kids.
Maybe he is telling the truth, maybe he is not for whatever reason. Could be he knows how you would feel about it. If his ex is out to get you, she will lie and what if he innocently mentioned to her you stopped drinking. Wow what an opportunity to wind you up to start again. Your priority is your sobriety and you give up now and she wins.
You need to try and calm down, breathe and most importantly don't drink. Whatever situation you are facing, sober is the way to do it. You need to keep that pride. Concentrate on your upcoming meeting, go home and find out what has been going on.
Good luck and know you are not alone. I for one will be thinking of you. Hang in there.