Thanks everyone for your generous responses! I am still pretty new to this world of addiction and recovery (despite having lived with an alcoholic for decades), so I'm trying to figure things out.
SoberLink sounds like a great idea - I will see if ex will do it. That would really provide an additional measure of safety for visits.
hopeful4 - my kid is very aware of what the parent is doing, knows what alcohol-related behavior looks like, and has their own phone to call me if anything isn't right. We've discussed contingency plans and what-ifs. Kid has told ex "if you ever start drinking again I won't speak to you for a whole year", and we've discussed relapses and slips. However, kid is still in that wishful-thinking phase where s/he believes that because their parent said they've stopped drinking, that means they really have stopped drinking (and ex is on best behavior when kid is around, as far as I know, and kid always comes home from visits in a good mood.
So kid is mature enough to be aware of their parent's addiction, but still wants that close relationship (especially because over the last year, parent and kid haven't seen much of each other because of parent's frequent moves). So I have a very mature and responsible kid (this wouldn't even be a question if kid was much younger or less mature), but I still worry about safety.
NewRomanMan: The information I have is that large quantities of liquor-store purchases have been made on ex's credit card over the last few months, when they said they were abstinent. When I've seen ex, usually at events related to kid, they've have what I've come to recognize as the I-need-a-drink look: very sweaty, tremors, flushed face. I am not sure about the other drugs. Ex has missed kid's events because "I took some medication for my back pain/indigestion/headache and it made me sleep all day", which I think means "I passed out" - which could be alcohol, drugs, some combination, who knows?
Ladybird579 - I've been pretty frank with kid about addiction and alcoholism, including things like denial, relapse, not blaming oneself for the addict's behavior, etc. We've talked about "early recovery" and how addicts often face challenges during this time. However, I haven't told kid about the liquor store receipts, and I haven't told kid about the financial troubles and the job problems because I really don't want kid to start thinking that it's one parent against the other one and kid has to take sides (this has been a dynamic that ex has used in the past - "it's you and me, kid, against the other parent"). . But maybe this is not the best choice? I'm open to others' experiences.
Many thanks again everyone. What a great community!