Is it permissible for a husband to divorce his European Christian wife after she confesses to adultery, and return to his country with their young son?

The wife erred by informing [you] of her commission of adultery, because the default is to conceal one's sins. Divorce is permissible, so if you divorce her, she has no right to custody, because the preponderant opinion is that Islam is one of the conditions for custody. If custody is yours, there is no blame upon you for traveling with the son; rather, the father has more right to custody when one of the parents travels. However, this should be done with wisdom and gentleness. Marrying a woman from the People of the Book is permissible, but it carries great risks, so a Muslim should not resort to it, and it is not permissible to marry her except on the condition that she is chaste.