You say she does not want more time...it is an "open door" per se. But this is your side and we can only chose to believe you...but with skepticism.
I am sure mom has a complet different outlook. Maybe this rational on you part is not apparent on hers...I am sure she feels slighted. It appears you are making every excuse why you should move, but no thought about the reasons you shouldn't move. (kids will love it, save gas money, she does not see them, she does not want more time)
The move may bring this to light with her. Bottom line, if the move is simply for a bigger paycheck...don't do it. I am telling you from experience. While I was 1500 miles away it severed my relationship with my dad. Whether it was his fault, mom's, mine does not matter. It is what it is. We have not spoke in 15 or 20 years...I lost track and ain't sitting by the phone!
Maybe there is an alternative. Perhaps dad can work 4 days with 10 hour shifts and drive the 4 days, be home for a full 3. Maybe he can get an efficiency apartment there and stay during the week. I would try these options, and explore others before you conclude the uprooting of the kids, impacting mom's relationship, and endure all the stress. No matter how you put it a major move ranks in the top ten Heirarchial list of life stressors...along with new job, death, divorce, move, illness, marriage, financial difficulties, and there are a few others. Moving and new job are 20% of the list...thought about that? Now encompassed with a possible custody fight? Driving the kids 100 miles one way? How much is this new job worth? Scorned by mom for the move and dealing with that resentment? Think about it.