Meadow - My heart goes out to you! Congratulations on 4 months of being sober. I have had my struggles with alcohol, I know what a terrible battle this is, as do others on this forum. 4 months is a huge accomplishment.
Keep the AA thing under your hat when you are around your committee or other witnesses in the future. The society takes a very dim view of AA.
Matthew 21 has the parable of the son that told his father he would, but did not and the 2nd son that told his father he would not but did. I love this parable! I would use it in your meeting. With a tear in your eye let them know that you feel you let Jehovah down because at your baptism you promised Jehovah you would, but unfortunatly you failed and now feel like the son who told his father he would, but then did not.
Here is to hoping 3rd time is a charm! Hopefully you can get back in and help get your kids OUT!