I would definitely try not to put too many expectations on this - I think telling the people closest to us is normally a good idea for lots of reasons (support, just honesty of where you're at, I find it harder to start drinking again if I've told people I stopped, etc) but they're entitled to have doubts and I think something I didn't understand the first time(s) I quit was that those people closest to us are dealing with their own issues and hardships, and also that I need to do what's best for me, for me.
even if they say something dismissive (and most closest to me have) it shouldn't impact me too much and I should just keep on doing the best I can
I've stopped trying to get people to see how things are different this time etc because time has taught me 1. Even I get that wrong and 2. They'll never be in your head so it will only ever sound like you're trying too hard to make some grand gesture that they've probably heard before
I vote be honest but don't pressure them to respond a certain way, and try not to expect too much