Am I permitted to emigrate alone without my wife and children, knowing that they refuse to emigrate and that I fear for my religion and the religion of my children from living in lands of disbelief?

The state your children have reached is a result of residing in lands of disbelief. Emigrating to Muslim lands and leaving your family and children is not the optimal solution, as it entails neglecting the trust and responsibility of raising children. For indeed, "all of you are shepherds, and all of you are responsible for your flock."

A Muslim chooses in their life between the better of two good things or the lesser of two evils. If you are unable to reform your children in your current location, move with your young children to another country where you can care for and reform them, or to another area amidst a Muslim community.

Your separation from your children and leaving them with your wife is a form of neglecting the trust. The more proper approach is for you to stay with them as a guide, disciplinarian, and advisor, striving to reform them, yourself, and your wife to the best of your ability, until Allah brings ease to you and to them.