This is an interesting development, and I'm eager to see how things pan out for you.
I am wondering, what do you mean by a legal way to reunite? are you hoping for citizenship from a country other than your own? are you referring to the legal rights that come along with being someone's offspring? Since the entire situation isn't very clear we can only speculate as to your motives, but the mention of attorneys tells me that there's perhaps more to this story than just wanting to see your mother again.
as for finding people in Japan, I'm not sure exactly how to go about that, or what the best way of contacting her first would be (I would recommend a heartfelt letter before anything else), but a tourist visa is the easiest way to get to Japan, and I believe will allow you to stay for up to 90 days (at least that's the case here).
anyways, good luck and keep us posted!