@Mark B - As much as it stinks having to re-enter the workforce, I think your plan is good to brush up on your skills and seek the highest paying position you can land, at least for a while. This will have two important benefits: It will give you the highest income possible, and it will also lay the groundwork for a potential reduction in alimony if appropriate. If you find a position paying as much or more than you used to make -- excellent! If you cannot find a position making that much (and please carefully document EVERYTHING you do to find another job) then you have all the evidence you need to support a reduction in your alimony payment. I agree that it could be difficult to get a reduction at this point, not until you have done something to regain your prior earning level, and day trading will not likely be viewed by the courts as a viable attempt. I paid alimony as well (though nowhere near as long as you but a much higher amount), and it sucks. Because of the iniquities in the system, after paying alimony to my ex, I literally was left with $100/month to support myself and two school-age daughters for three years.
YMMV, but I would not consult with a new divorce attorney until you have exhausted the job search and obtained the best salary you can get. Then you can go for a reduction with all the new circumstances at once, because as you likely know, you can't waltz into the court every time there's a minor change here and there. Make your next attempt count, you may not get another one. And if you are unable to command a high salary as before, your ex may be more willing to negotiate a reasonable settlement than you relying simply on trying to prove she's funneling money elsewhere. Her attorney will recognize you have a strong case that you have done everything you can to maximize your salary, and will counsel her as such. Also I would expect to impute a reasonable income to her, as everyone needs something to live. If she claims she has zero earnings, that should fall apart pretty easily.
Definitely do the math on the rent vs. keeping your house scenarios. If I'm understanding your expenses correctly, your out-of-pocket mortgage payment (after renters have offset some of it) is $1400-1500/month. Add in any additional insurance/maintenance/taxes/etc. costs, subtract any tax breaks from writing off interest and taxes, and determine if you could find a better alternative renting with your dogs. It may not be possible in SoCal, so maybe that will give you some comfort knowing the house may not be such a bad alternative after all. And of course you stand to gain from the increases the housing market right now and hopefully in the future, particularly in SoCal.
You've already heard it from others -- I'll pile on and say that day trading should be nowhere on your radar until you have enough money you would feel comfortable putting in a bag and setting it on fire. Stick to prudent investing. Then when you've accrued $1 million, decide if you want to venture back into day trading. As already pointed out, it worked for you -- until it didn't.
Good luck, keep us posted (maybe we should start a separate thread and not hijack this one for future updates)!