All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We ask Allaah to reward you with the best for taking care of the two step-children, and for your great concern to raise them according to Islam. Basically, you are not obliged to let them live in your house, if they have anyone who can take care of them. If there is no one to take care of them or that person is not eligible to do so, for instance he/she is non-Muslim (the caretaker should be a Muslim as some scholars say) then you must permit them to live with you according to the opinion of some scholars. In this case, you have to do your best to guide them to virtue and to provide them with the Islamic environment that will help them be righteous. They are still at the stage where they easily accept your guidance. You and your wife should set a good example for them, choose pious friends for them and marry them off to pious mates when they reach the age of marriage.
Probably, it is more suitable here, to remind you that living in a non-Muslim country has bad consequences, particularly on children. Your wife's children are a living example of these consequences. How can then you feel safe regarding your own children? The best solution in this matter is trying to migrate to any Muslim country with your family. This may help both of you to raise the children according to the teachings of Islam.
Allaah Knows best.