I think that establishing that he is totally sober will just take you down the rabbit hole of monitoring constantly (and arguing constantly, and eventually spending lots of $$ on lawyers). The best you may be able to do is to require "continuous disclosure" of his alcohol intake during parenting times (so - breathalyzer testing before, during and immediately after any visits, at two -hour intervals). What he does outside of visits is up to him. If he manages to fulfill these expectations for six months (unlikely, as he seems to be going downhill rather than up), then you can talk about expanding his access to Kid.
The exception to the whatever-you-do-on-your-time-is-your-business rule is "alcohol related incidents" - in my order I defined those as anything which involved first responders (so car crashes, DUIs, seizures, domestic police calls, etc) which a reasonable person would believe were related to his consumption of alcohol, or anything which would have placed Kid at risk of physical or psychological harm had she been there when it happened. An "alcohol related incident" sets the clock back to zero, as does failing or skipping a breathalyzer before/during/after visits.
(I'm quoting all of this from my own court order).
I'd stay away from requiring attendance at AA meetings. Easy to fake attendance (you can buy 30-day chips on eBay), hard to prove someone is or is not attending an anonymous fellowship. Also, do you really want to inflict a(nother) drama-prone self-pitying drunk in full creative-denial mode on your local 12-Step group?