medical insurance
Consider acquiring some supplemental medical insurance for your family, I think. Emirates has a long-established tradition of taking very good care of pilots with lengthy illnesses but I don't know if that has a counterpart with family members.
Your family's coverage is limited to a certain maximum cash amount of treatment every financial year. I am too lazy to look it up but I think you could easily run through the mentioned amount in about six weeks if they were unlucky enough to be hospitalized whilst visiting the USA.
You can buy 2.5 million dollars a year coverage online via BUPA for a token amount and you will have peace of mind for any lengthy health battle which (God forbid) your near and dear may experience. If memory serves it was about $300 for the kids and about $1800 for the wife per annum.