Is it permissible to apply for Canadian citizenship for one's wife, knowing that the naturalization ceremony involves pledging allegiance to Queen Elizabeth?

The fundamental principle is to prohibit residence in non-Muslim lands, except for the purpose of establishing religious rituals, ensuring protection from temptation, out of necessity, or for a benefit such as da'wah (inviting to Islam). It is permissible to apply for foreign citizenship if it does not entail corruption, such as contradicting Islamic rulings, and if it achieves religious or worldly benefits. The questioner may submit an application for his wife to obtain citizenship if she can avoid taking an oath of allegiance or if she qualifies her oath in a way that does not contradict Islam.