Anyone who is a parent will know that the father as well as the mother must sometime make sacrifices for the good of the family. Your situation shows your determination to fulfill your family obligations -- congrats on that.
I agree with PG that the detail can take up a very few lines (minimize this, don't overdo it) in a cover letter. Your child was diagnosed with a health problem that not only required immediate action, it required a shift in geography. Show by your letter that you have all intents to now refocus on the career and put just as much passion into your work as you put into your family.
On the CV, I would show the PhD as interrupted due to family health issue and subsequent move to the USA, but otherwise avoid too much focus there.
“Humility is not my forte, and whenever I dwell for any length of time on my shortcomings, they gradually begin to seem mild, harmless, rather engaging little things; not at all like the glaring defects in other people’s characters.” - Margaret Halsey