Pin Head,
From day 1 until getting checked out on the line will take 6-7 months. FOs do a little less line training than capts, hence the difference. During this time you normally get to go home once for approx 10 days, normally after the ATPL test/medical and prior to line training. Obviously things vary and some people have less time and some more at home during the training but that is the basic plan. The Company pays for your wife's flights and accommodation for 2 periods of 7 days during training and once for your kids' flights and accommodation. So, basically, your wife and kids get a holiday in Japan for 7 days during your training. It's up to you to figure out when they will visit and, no, the Company does not specifically give you time off during their stay.
Widebody,
I reckon your experience would stand you in good stead for an FO application. There have been people without type ratings and some who have barely qualified on type, so your 1500 hrs isn't bad at all. I'm afraid I have no idea what's happening with the waiting times. What with every airline going belly-up in the States and the disease now spreading further afield, AJV/AJX can afford to be more selective than before (lucky some of us got in earlier) and I suppose the waiting times will go up. I think they will look more favourably if you're able to come as soon as they want you but they do understand the norm of 3 months notice to most airlines, so don't sweat it if you have to let your present bunch know you're off.