What can a wife do if the husband blackmails her with her sister's photos and passes them around to her family and community? Should the wife leave him to protect her family’s honor or stay in the marriage for the sake of her kids?
I am sorry to hear about this situation. This is certainly despicable behavior from him and a breach of trust.
It is difficult to have a marriage without trust. However, it is your decision whether or not you wish to stay in the marriage.
None of us here can give you good advice on whether or not to stay in the marriage without knowing your situation (both personally and also in terms of practical matters). It is best if you can discuss this with people who you know in person whom you trust, such as family or people whose advice you respect.
Wishing you the best either way, and sorry you have to go through this.