A lot of enterprises that are terrible t work at won't even pay for that kind of self development because they're so dysfunctional they can't put the money towards a solution after decades of being in a form of survival mode. I don't know what situation OP is in specifically wrt the organizational dysfunctions but I can sympathize very much with feeling entrapped and can only imagine the pressure with children involved.
The first thing I'd recommend is solid at-work time management - your goal should be to do the bare minimum to do well and make steady progress there in terms of you literally doing nothing but somehow being essential - a lot of managers do this after all, why not make it factual instead of how you perceive your job? But your heart and focus should really be on getting out of there and possibly using your side projects as evidence, not your day job (you're likely working on code that is far below your capabilities partly because you're too stressed to take on effectively now btw).
Most people besides your peers will have trouble understanding how tough it can be to be a breadwinner stuck at a job that's a deadend when you have so much passion to do better, so staying connected with people that can inspire you is critical. I'd say it's probably kept me from going completely insane and doing things I'd really regret just out of sheer frustration.
Exercise helps with few doubts but it won't help much unless you're managing your time effectively to keep the stress and workload at bay so you don't die of adrenal gland failure or something asinine.
Keep your head up and try to record your progress for yourself and try to limit work to side projects that do go somewhere and really understand what a minimum viable product means and take it from an entrepreneurial approach than engineering one.