Is a wife considered forbidden to her husband if he writes to her, "Are you forbidden to me?" without uttering it verbally, and he intended the question itself, not the pronouncement of prohibition?

A husband's statement to his wife, "Go to your mother's house," and the writing of divorce, are both allusive (kinayah) forms of divorce, by which divorce does not occur unless intended. If your husband did not intend divorce, then it does not occur.

It is incumbent upon the spouses to understand each other and resolve problems away from divorce, especially if they have children, to avoid negative impacts on them.