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You can give a promise to the court (an undertaking) which promises that you would not drink whilst the children are in your care. This would be a promise not to your ex but to the court and you could be in contempt of court if you breached this order.
In the nicest sense there isn't a lot more I can say about an undertaking. It would however be sufficient hopefully to give them the assurance which they need. I hope that this helps and please can you rate positive.