All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
Undoubtedly, the role of inviting people to Allah Almighty and teaching them about their religious duties is significant, especially in communities where Muslims are a minority. If a woman can fulfill this role without neglecting her household responsibilities, her husband should support her in this endeavor, as it may bring blessings to him, his family, and his wealth.
It is advisable for spouses to discuss this matter and weigh the benefits, as the wife may be able to persuade her husband and resolve any concerns.
Should the husband persist in his refusal, the fundamental principle is that she must obey him and not leave the house without his consent, unless the duty to practice Da’wah and teach others is an individual obligation upon her. In such cases, she may depart without his permission, but we think that it is unlikely that the matter will reach this level of obligation.
However, the two spouses might explore the possibility of fulfilling this role through the internet or similar means.
Allah knows best.