Welcome to our forum.
People don't always find out about (or come into) polyamory neatly and cleanly, so you aren't alone in having hit some unplanned speed bumps. I'm glad to hear that your marriage seems to have survived the speed bumps, and come out in one piece.
Be sure to always give your marriage a high priority, as NRE (New Relationship Energy) with J can sometimes skew your perspective on things; it's just something that happens to people. So, be aware of it, and remember that G will probably need quite a bit of extra reassurance in order to get used to this "strange new relationship model" without feeling threatened by it. Kudos to him for being willing to consider polyamory, in spite of his initial misgivings.
Just take it slow, would be my advice. Baby steps. And a lot of communication along the way.
With the two kids involved, there's a lot at stake, so study and learn as much as you can about what polyamory is and how it works.
Glad to have you here amongst us.
Love means never having to say, "Put down that meat cleaver!"