I have received a good job offer in another state. Can the family move for the wife's career?

There is no objection to a family moving for the wife's opportunity, as long as the decision is made together and everyone's best interests are protected. A move affects the husband's career, the children's schooling and closeness to the extended family, so weigh all of these openly. The Qur'an praises matters decided “by mutual consent and consultation between the two” (Surah al-Baqarah 2:233). If the husband has to change his career, appreciate that sacrifice just as a wife appreciates it when she has been the one moving all this time. Visit the new place first if you can, and plan the transition for the children. A decision both are content with is more blessed and easier to face. See duties of husband and wife.