Welcome to FT ScotttheNovice, and no, you're not a numpty, you're just on a learning curve.
I do think you should re-read the master sticky at the top of the forum. It is very comprehensive, while I appreciate there's a lot to take in you'll find most of your answers there. In your position, with a family in tow. I think you should consider beginning your journey ex Dublin, this saving on UK air passenger duty.
CO (Continental) has flights to Newark (EWR) and onwards to all points in the US. Availability is patchy, but a quick look has shown up several possibilities, though admitttedly I haven't spent much time on ANA. You can get to Dublin cheaply on Aer Lingus, Ryanair or even BMI if you're lucky !
I'll leave it to others to post further advice, and do let us know how you get on. It's always nice to hear the resolution.
Finally, I was a newbie once - FT offered me opportunities I could only ever have dreamt of - am off to Costa Rica next week, with Mrs Grantosol, flying business class all the way. Cant wait !
Grantosol