Still unanimous: do tell your husband, but unless it seems terribly important to him (I would be surprised if it did), write to your sister-in-law. You might compromise and send it just to her, not to them both (and any children) as you might otherwise have done.
My preference would be to write her a note, not send a printed greeting card -- this is such a close relationship, not just a work colleague or neighbor. Don't mention the rift in the family, just tell her how sorry you are to hear that she lost her mother, something nice you remember about Mom, how proud you know she was of your SIL, and your sympathies to the whole family. Four sentences, 10 minutes, and Hallmark can't come close to it. If you or she really love greeting cards, you can choose one with plenty of empty space and write your message, but stationery or a note card is just as appropriate and more personal.