I agree with Taking 5...
Stopping drinking is easy! Promising to stop drinking is even easier and A's promise the moon when backed into a corner.
What you are looking for is a man who is trustworthy, connected, invested, loving and has your relationship with you and your kids as his number one priority. That is impossible if he is drinking so sobriety is the cornerstone of that possibility.
However, sobriety is just not drinking and recovery is learning how to live and thrive sober and find true joy, peace and purpose and meaning. For most that make it (and the numbers are few) it requires a lifetime of working on themselves and their character defects, FOO issues and any other core reasons they use drugs and alcohol to cope with life.
So... you are wise to consider that words are not guarantees of true change and even if stops drinking it may not bring the "happily ever after" you have always hoped for.
Alanon, alanon, alanon...books on addiction, counseling can all get you lightyear jumps to finding your personal path and true happiness....with or without him drinking or not.