My parents used to be very much on my case, albeit in a different way, but I felt similarly.
I got a great job and career, and, unfortunately, I was recently laid off.
When I told my dad, he wasn't disappointed or mad at all, he was sympathetic. He knew I can take care of myself and be stable. And, although I'm planning on take a couple months off from employment (I plan on working on game dev and music), he's not worried about it because I've proven to be very financially stable, I don't have bad habits (I don't drink casually nor very often, I'm not a huge spender, etc.), and that I have a desire for results.
I've seen a bunch of your work and it's incredibly impressive, not to mention you've shown ability to collaborate with other people to create stuff for them. What sallpal said is an opportunity you should take. I've been to quite a few cons similar to that (Comic-Con for several years, APE also for several years), and that kind of art really sells (to be honest I'm confused by it but it's not something I know much about).
In my view, what you need to prove to your parents is this: to stop drinking, to show that you're actively trying to save money, and that you ARE making money. owl already mentioned one good way of that (and yes, it'll suck, but the majority of people have to start somewhere). Another you could do is to start selling prints and the like. I think you're capable of doing so, especially if you work on marketing it. Unfortunately I don't know much about selling art.
Hope that helps.