I assume your kids are young and that they are not going to be spending much time in the lodge bar. Make it a good ski trip, ski hard get the most out the lift tickets and hang out with the kids . Plan to get to bed early and back on the slopes early. Play games or watch movies at night, the AV is the only thing that thinks alcohol is so important that risking having too many and ruining a good trip is worth it.
If you do promise yourself right now that you won't drink on the trip, you can guarantee yourself that you won't risk having a 'bad' one.
wish you well, ski hard have Fun