I hear you on the early/mid 30's career path change. From what you said, its impressive you are where you are and have a good salary. Remember, starting 'over' in a career can be very stressful as I have experienced doing the same thing. I actually went from engineering into software, which one could call a lateral change...but the subject matter was sufficiently different to be considered a full on career change!
A few points on the actual coursework. First, undergraduate curriculums are brutal. You really have to be engaged in it unless you are one of those math prodigies who simply can understand advanced topics such as differential equations or thermal systems with very little effort. Most of the time, you will feel dumb but it's doable. That said, when you already have a good career as you do, its easier to get into a 'fallback' mindset where you get to a certain point in thinking that its not worth it. As an undergrad, I had no such concept so that upped the desperation factor a bit when the work load was overbearing. You might handle it well, but just some aspect that I figured was worth mentioning.
Onto that point, assuming you complete enough of an engineering program to get hired, you'll have to forgo salary, benefits initially which in itself is tough. I did this to change into software, and still earn less than I did as a system engineer. While fleeting, I have contemplated switching back, but I like what i do now a lot, and the opportunities both professionally and as an entrepreneur help me push through the drawbacks. If you switched into engineering, you'd likely be underwhelmed initially by the work unless you land a technical job for dod or doing really cutting edge research. Most of my engineering friends don't really use what we learned in college, but some still do. So with that said, pick *relevant* subject matter to pursue - my friend who works with lasers and systems does all sorts of FEA, and R&D stuff which seems cool. If you have an idea of what subjects within engineering you like, you can send me a PM and I can try to give you a brief overview of what fellow engineers do to give you a perspective.
Engineering is more of a mindset than having a particular set of skills. Its a relentless attention to details, and a constant feeling of not knowing things, and feeling inadequate at times. Pressure can be tough depending on the job because people outside of an engineering department will discount the difficulty at times. As our sales team says when it comes to our product, "Its only code".
Lets assume you want to change. Which field should you pick? I was mechanical engineering, but those kinds of jobs aren't in as strong demand as decades past. Mechanical engineers usually do systems engineering , design engineering (CAD work), or more R&D roles. I know less about electrical engineering, but I think it would have a strong component of coding and I&C work. I know a lot of chemical engineers that landed into systems level engineering too. Finally we have software engineering which is the most in-demand field right now. Web development is strong, but software engineers with a strong understanding of OOP, and embedded systems are in demand.
If you have questions, feel free to shoot me a PM. I'd be happy to help. I left a lot of stuff out above, and simply gave a brief overview on what I know. I am sure I missed a lot of stuff!