Just do not go.
Every single aspect of it spells disaster.
Firstly, a move like this is HARD. Really hard. You've had posters on here saying they bailed out as it was just too much even when they were totally 100% behind a move and WANTED it. You don't want it - more than that, the good things in your life are here (your Mum, your life, your friendships, your settled secure situation for your children... everything). The chances of you going, finding a great life, being happy and glad you went are vanishingly small. It's clear you know that. The only emotion pulling you there is guilt - 'what about the children?' - but that's misplaced - I can't think of a worse situation for them than to be uprooted from home, granny and schools and get to see you miserable (and they will see and feel this) and see even less of Daddy as he's in work in the big city until after they go to bed.
Secondly, the offer sounds crap. Lots of folk who know what they're talking about have come on here and NOBODY has said 'that sounds decent!' - but plenty of folk have said, 'that sounds crap/get it upgraded/hmm surely the package must be more in practice than that'. Not good. Even less good when you've got a DH sitting in his office with his tongue practically hanging out with desperation to go. They will know that. It might be the reason the offer isn't higher. At the very least, he sounds naive and inexperienced - not really the kind of person I'd be pleased to junk my job for and end up dependant on when his priority seems to be not getting the best deal for his family but whoo, I wanna work in NYC! Oops, I'm on the US payroll and I've got no holiday time and eeek, they won't actually pay for us to get back and we can't afford to go for at least three years, you're just going to have to suck it up darling. By the way, I'm having a great time...
Thirdly, your DH. I would think that the single most important factor in a move like this being a good idea - for you, for him, and most of all for the children - is you and he being rock solid. A team. You'll only really have each other at first. Worse than that - you'll get there and while you stay at home with the kids, he gets swept into a new life, new work friends, all the excitement. He's not there for you now. How do you think he's going to be when it's a toss up between coming straight back in the evenings because you're alone and have had the kids all day, and going for drinks in a cool NY bar to 'get to know the team'?
The biggest red flag in your posts is the way your DH is presenting this to you. If he were on your side, if he saw you as his partner, his co-parent, his equal - then while he might well be enthusiastic about going, he'd be mighty concerned about you, how you felt, whether it was a good thing for you (and therefore the children, largely). He's not. In fact, he's actively trying to present a very average deal to you as a huge moneyspinner, when my guess is that he knows full well that won't be the case. As you already know, he does not have your back. He's on his own team, not your family team. If you go, you will be under pressure, and alone. And he will not be there for you, listen to you, or probably let you go back without a fight.
All this is even before you consider the idea of whether you like the idea of living in the US, paying for healthcare, having your kids in the school system there...!
Say no. One big fat no. My guess is that he will go anyway, and you will split - I think that from everything you say, it's quite likely. Just do not make the mistake of going as you fear him bailing if you don't. The alternative is a lot worse.