First, don't give up and don't think you're stuck in what you're doing now! I don't know what I can suggest you about your present job but maybe you're taking too much on your own. It's not healthy indeed to stress so much about your full time job it affects your evenings and nights. That's the kind of worries that are usually more common for entrepreneurs. The only tip on this is maybe ask more for help; maybe your team or manager are pressuring you a lot but you can still slow down the pace a bit and see how it goes. A lot of time, for high achievers, their own perception of how they're supposed to perform is the enemy but often, people around them are not expecting so much from them. You obviously got some skills and they appreciate your work if you're still working there.
Second, about your dream career, design, it's still there. If it can give you some hope, know that having a good technical base in design is awesome; design itself can be learn through experience and practice but the technical part is harder to learn if you never had any method to start with. So what you're learning right now at your dev job and also the training you already got from school will be great tools for you. The design part is often a matter of how much you practice and how much passion you put in learning more techniques. If you want to do design, find as many small opportunities to train your skills and stay up to date with the technology.
What you need to be careful about is to never stop creating design, to not lose the touch with that field. The only advice I can give you to start moving forward to your new career or at least to keep your design skills is to find some small projects that are not urgent and that won't interfere too much with your lifestyle and your family life either. It can be projects for yourself too. Plus you don't know, maybe at your work now, they could need some dev who also have more design skills. That's a very powerful set of skills together even if you prefer the design part! Few designers have that kind of background, it will certainly be useful for you and that's how you should see it. See what you're doing now as a transition period.
Obviously, you can't simply quit this job because you're the one supporting the family but every big artist and successful leader didn't let that stop them; they simply added a bit more every week or every month to their schedule until it was possible to make the jump into their dream career. Don't let your "unfinished" training stop you, it's not a guarantee of success or talent at all. Talent itself is a myth. It's practice that makes talent. If you can, find some small side projects in design, build a portfolio slowly, work for community projects if you don't want too much pressure but great opportunities and don't put yourself in a gloomy mindset. You'll see more opportunities if your mind is clear and you'll also find it way easier to create and find solutions to your dev issues!
To find some extra projects in design, as I suggested you can find community projects; they always need some help. You can also find some local businesses and either offer low price design work or even free ones if you only need to build a portfolio. You can start your own projects for yourself (eg. youtube channel) or find a special idea you could offer to a specific target market (eg. animation for business, intro of videos for speakers, custom intros for Vloggers). There's always freelance websites but they can be very demanding in time and energy, so be careful about them. Since you do some web development, you could always build yourself a nice designer website and start offering your services, and use that platform to refer potential clients to. Get into business Facebook groups and on social media as a professional. If you don't mind doing some Skype or phone meetings, clients really trust designers a lot more when they can chat to them directly. Making this option available is really good. If you keep designing and testing yourself on side projects, one day you may see that you're good enough to just jump into freelance full time or find another job with more design opportunities; and you'll also have something to show. From your comment, you seem to need to build your self-confidence about your skills as a designer and once that will be done, your options will seem more obvious and you'll certainly have more too!
I mention "design" but it's the same for your visual effect career. In fact that's a field that is in very high demand and you can use a platform such as Youtube to promote your work; you might even create something that goes viral.
Edit: There's also photographers you can contact; they often get asked for wedding projects and video montages. Not sure if it's the visual effect field you would work in but that's another place to look for work since they often do the filming but can't always do the effect part.