Dude! Slap slap! I did that. It doesn't work. If she wants you back bad enough, and you were going to leave your wife anyway, then yes I would do it with a commitment from your long-lost love.
But if you plan on dumping your wife and kids and run off chasing this girl you haven't seen in 13 years, sight unseen, I'd say exercise some restraint and caution.
I have to ask, "What was this long-lost girlfriend doing for the last 13 years? Why wasn't she out searching for you?"
Answer: Right now you're convenient. You're 700 miles away (so you are not a problem for her or a distraction), and a big plus is, you're still married so there's no pressure on her to pick up where you left off 13 years ago.
I would have to say, I'd have to be damn sure about this. I know its like you want to do this. I can understand it perfectly. Just don't rush in.
If you make that big, big mistake you will ruin what's left of your life and your long-lost love may just leave you in the dust and not look back.
The other thing is, can she respect you if you leave your wife and kids for her? Some women consider that to be pretty damned awful.