Good for you for getting yourself and the kids out. The fact that he is so arrogant about drinking whilst he has no drinking as a bail condition speaks volumes.
LTD is right, you don't need to rat him out. I know that I would feel tempted to do so in an attempt to get him to just stop drinking already. Given that you have heated arguments already, I can't see what would be gained by raising the stakes at this stage. No reason why you have to lie if questions are asked under oath, though. In fact, I would say that it is your duty to yourself and the court to tell the truth. Lying under oath is a serious matter. Whatever consequences are due to him will occur, especially with his attitude. It may be now or in 10 years time, but until he gets some awareness and humility, they are coming.