For me whether you are being unreasonable or not would hinge on a few factors:
Your children are at important ages, one on the precipice of GCSE’s, one at the start of their secondary education where friendships which will important to them in the next few years are going to be formed. How confident are your children socially and academically? What are their future dreams and ambitions - would a change in schooling support these or impact them in the future possibly?
Are you or your husband the breadwinner? Will you be able to survive on your salary alone if your husband is unable to secure work? Will he be able to easily and quickly secure work on return to the UK if you need to? Will you be able to have the same living standard in the US?
Have you sacrificed for your husbands career? Is it “your turn”? Would the impact this would have on your career supersede any financial benefit to your husband’s career by staying here?
Do you own your property? Would you be able to get out of your rental contract easily if not? Would you be able to rent out the property easily if you own? If the contract is cut short and you need to return to the UK, will you be able to secure a new rental easily, or evict tenants easily? It would be potentially very hard to secure short term tenants dependent on area you live in, and if you can’t that’s a bit of a gamble. If your contract is cut short you then have nowhere to return to. What would you do in terms of renting property in the US? You may be locked into a long tenancy which you then need to continue paying for and a contract that is cut short. Alongside this what would you do about furniture and personal possessions storage?
Have you/your husband got any loved ones who are unwell or unable to travel easily? If not, how would you/your husband/your children cope with missing them during this time? Would finances allow trips home for example? Would you have the space out there for them to visit? What about pets?