Yes and no.
Studies show that after a certain point--something like $75k/yr--additional money does not in fact make you any happier. Below that mark, less money could potentially mean less happiness (mainly due to stress over money), although do note that everyone is different in that regard.
You also need to realize that nothing is worth a job and career that you don't like. What's the point removing stress due to money if you're just replacing it with stress due to hating your job?
Besides all this, remember that it is your life. Your family won't have to live with the consequences of your choices; you will. Your family won't have to get up in the morning and go to your job; you will. Your family won't have to deal with your boss, your coworkers, your career; you will. So don't let your family's ideas of what will make you happy dictate your choices.
Can you find a middle path? A way to both make a decent living and do something you love?
There are a few possibilities. One is to find a career that is not life-consuming (read: not a doctor) and leaves you free time to pursue what you love. One is to find a way to make what you love a viable career--this is difficult (can it even be monetized?), and probably requires some sacrifice (i.e. stop buying videogames and iPhones and so on all the time). One is to defer doing what you love, though that's a huge trap. You might consider reversing that--go on your JET program, take up a "normal" career when you return.
I dunno, I'm just throwing stuff out there. The upshot is, make your own decision, and try to hedge your bets.
