Dating someone in recovery?

Hey, I could really use some advice or input.

So I've been talking and seeing this guy for about 18 months now, I'm 25 and he is 31, we met in a support group for amputees. I have a very hard time talking about things but he was just so easy to talk to and very friendly, we clicked and we started hanging just as friends for awhile and then it started to become more flirtatious and then we stated dating. We both are single parents with kids the same age, we are both our children's full time, only parent so sometimes we don't see each other a lot, we have been taking things very slow mainly because of the kids and that is fine with me. I don't date a lot, so I'm in no rush. But recently around 5 months ago he told me he was going to quit drinking and has been in therapy for a lot of things he needs to work on, I was kinda surprised about the drinking, I knew he drank but he was very causal about it and I have never seen him drunk, he said he doesn't really get drunk, he just drinks to cope. My roommate explained that he is probably a functioning alcoholic. Anyways we kinda slowed things down more so he could focus on his sobriety, we hang out every so often, and we talk and text everyday, we don't have sex and occasionally we will go on dates. My roommate has her concerns but she also really likes him, we are both just torn on is this like a huge waving red flag and I should run because people don't change or do we keep doing what we are doing and see what happens? I do want to add I have my own share of struggles, to where we can't hang out because I'm sick or I'm in the hospital and have lots of testing being done. Which is why I haven't dated much in the past because most guys run when they aren't getting my time and he isn't like that at all. He's supportive and understanding.