My friend’s husband shows annoyance at her when she goes out for Da‘wah activities, but this reaction doesn’t lead to any chaos or bigger problems in the home environment. So how important is a mere temporary displeasure and just a few taunting sentences which she tolerates with patience and carries on?
I think she can decide best what is appropriate for her while giving due weight to the harmony that should be maintained between a wife and her husband. If she believes that her decisions would not disturb the atmosphere of trust and faith, she is perfectly allowed to do what she wishes to.
However, I personally feel that sometimes things keep boiling up within a person till such time he/she can no longer bottle them up. Then small exchanges of some disapproving sentences take the form of full-blown disagreement which leads the victims to excessiveness. I mean what your friend wishes to do is not a program of one or two days. Is it? She wants to continue it. That ultimately means that her husband will continue to observe that his wife is constantly disobeying him— according to his viewpoint. I fear that these small taunting sentences then may turn into complete disapproval which obviously can affect their relationship.
What I do not understand is her hurry to do everything her way: she should first convince her husband regarding the importance of learning and teaching Islam. In the life of a couple, there come many occasions when no request is put down. I advise her to wait for that moment and, as it comes, place her request before her husband, which I believe he would never put down. I am asserting all this because the process of learning and teaching Islam requires peace of mind. This is indeed the toughest path to tread, you would agree. Let her settle down the matter with her husband happily and peacefully. Then the world would be open to her to work with utmost peace of mind.