The first option is clearly the most realistic - although it hardly feels like a fair contest since the second option is about as realistic as me claiming I hopped on a magic carpet to mars last night to go play bass for Elvis as he reherses for his big gig on Saturn next month.
Which is to say "not at all realistic" (I mean come on.. me play bass guitar? - totally absurd!)
Something I think is missing from your plan is:
"Working from home" != "Working whatever hours you want"
Typically you'd be expected to be available as required during the day for phone calls, meetings etc.
Also unless your research is in the area of time travel you aren't going to have enough hours in the day, even if university "only" took 6 hours of your day (unrealistic for post-grad courses in my experience - expect more like 8-10 for a decent masters), by the time you've added on 8 hours for your "day" job you're already at 14 hours. You're going to need at least another 6 hours for sleep and that leaves you with a mere 4 hours for everything else, eating, washing, doing the boring domestic things like laundry and shopping for food, seeing friends/family/loved ones. It's a one-way express ticket to burnout! And burnout is not a nice place to visit let alone live!
As I mention earlier the first option is the more realistic of the two you mention - however I'd like to throw a third option into the mix. Consider finding employment and then rather than proposing working from home to enable you to study propose a shift to part time instead. Not everyone will go for it - and it will require a bit of schedule juggling with university but it could be very beneficial to you and potentially to the company as well. I was once in very advanced discussions with my then employer to carry out a PhD research project that was also an internal project for the company and they were very enthusiastic about the idea (here in the UK at the time it would also have entitled them to some fun tax breaks which no doubt contributed to their enthusiasm!) so there are ways and means that don't involve burning yourself out or having a low-paying research assistant job that mans you can barely afford to go to classes.