I'd try flying but carry a TON of brand new stuff the girls have never seen and don't see until they are in the airport and on the plane: Books, coloring books, games on your phone or computer, a new stuffed toy each, stuff to do with their hands. Carry a lot to distract them and even then, pack a ton of patience.
I still think it's not advisable to fly over Thanksgiving, period, ever. And I think you are still adjusting, yourself, to the idea that kids this young must stop very frequently -- it's not what adults are used to doing and you're seeing it as a time-waster when it's just how things have to be....But you can try flying this time IF you embrace the idea that a delay in flights could strand you all in an airport and you can be more patient with that than with stops on the road.
Bigger picture: This would be your seventh trip in about seven months from what you describe.
Think about it. You're making this long drive every month on average. In all seriousness, if you and your wife truly are this close to her family (and you don't have a family on your side), have you considered moving up where they are? It truly sounds like it would be good for you, her and your kids, and would stop the stress of traveling this often. If a job is the issue, yes, that makes things tougher, but you could at least start planning now so that eventually you can make this move even if it means a few years of prep to change jobs. Moving to be closer to your wife's family sounds like a better long-term plan since you say yourself, "I don't see us ever spending less time with the family."
You're new to parenting these girls and right now they're young and pretty much go where you tell them to. But eventually they will be the ones whose schedules take over more of your time. Before you know it, your girls will be involved in school events, Girl Scouts, church groups, sports, dance, whatever - and you will find that you will indeed be making a lot fewer trips because the girls' interests, things that make them who they are, mean you have less time to travel. So that's why moving could make sense, before the girls are forging their own interests and activities and you hear, "But that's the weekend of the church campout/dance recital/soccer tournament--we can't go to NY that weekend!"....
Also, if you are closer to the relatives, then relatives would be close enough to come to YOU to see your kids in recitals, or school plays, or playing sports. Wouldn't that be great? ...I know, the question was about flying and I answered that, but just wanted to note that with a closely knit family, if you can get up there before your girls are a lot older, you and the girls and the relatives all may benefit.