"I don't think she needs to be solution focused when the best solution is not create the problem in the first place."
Totally agree! For starters I'm finding it VERY hard to believe that he's actually being "forced" to take this "promotion" with no extra pay! Employers - even with the serious erosions in employee rights - cannot do that!
I still strongly suspect this is op's dh's attempt to dip out of parental responsibilities and coerce op into becoming a sahm against her wishes - just to be absolutely certain (because we've had posters do this before - calling a dp dh!) are you actually legally married? Because if not it's a definite "hell no!" Because you'd have zero protections if everything goes belly up! I think op should do some digging to find out if this REALLY was dh's employers suggestion or if dh has requested this role - do you have any contacts with his workplace op?
Even if you are married, this is NOT what you and he agreed! You had those 4 DC on the understanding you'd properly co-parent and neither would be away for work reasons more than X amount - and frankly he's bloody reneging on that!
In addition if his employment really is SO precarious that he feels he isn't in a strong position to say no to such requests from his employer, if it's an industry that's currently struggling (which the lack of pay rise would suggest is the case) - then actually that's even MORE reason for op to keep her job in case dh is made redundant! Might be worth pressing this point with dh and VERY carefully noting his response.
Ultimately there is ALWAYS a choice. Nobody can actually be forced into taking a certain job or position. As I said I'm really not convinced there's not at least an element of his WANTING to do this and be away from the family so much.
Also, slightly off topic but how come you're living somewhere so rural? Is that where "home" is or has that been a choice you've made and if so at who's suggestion? Because to be quite honest with 4 DC, I live rurally though not quite as cut off as you are and only have 1 DC and it is murder as they reach the preteen and teen stage as there's so little for them to do - and idle hands can be the Devils plaything to be honest! Where I live there's high crime, high drug and addiction issues and even the good kids act out occasionally out of boredom and frustration. If you can, I would recommend moving to somewhere less cut off.
I really do think he's taking the piss and you op need to not take this lying down!
HE Is the one that's trying to move the goalposts!
As I think I said in my earlier post, it is NOT his turn it is his kids turn! HE agreed with you to have 4 kids and not to do a load of travelling, completely out of order to drop this on you now!