Is traveling to work in Saudi Arabia—out of a desire to raise children away from innovations (bid'ah) and closer to the holy places to facilitate Hajj and Umrah—considered a disregard for the blessing of success and ease in one's homeland, and is there sin in it?

The profession of medicine and the call to Allah are communal obligations (fard kifaya). Hajj and Umrah (definition) are individual obligations (fard ayn) for those who are able. Raising children upon righteousness and away from innovations, if that becomes a means of their reformation, is among the obligations. Therefore, your departure to Saudi Arabia is not a sin; rather, it is an obligation upon you to perform Hajj and Umrah if you have not already done so. After that, compare the benefit people derive from you in both places, and reside where you are more beneficial.