Does a divorce take effect when the husband says to his wife: "If I find out you did such-and-such, it will be the end, and I will not consider the children," and is it obligatory to inform him of her doing this thing if new problems would arise from it?

Allusive divorce pronouncements (Kinayah) result in divorce if the husband intends to effect it thereby. The husband's statement "this will be the end" is an allusive pronouncement, and its meaning depends on his intention. This phrase could mean a promise of divorce, in which case nothing occurs, or that he intended for divorce to take place upon the fulfillment of the condition. The reference point for understanding his intention is the husband himself. If the wording was "if I knew... etc." and he never actually knew, then no divorce occurs. However, if the wording was "if X happens... etc.," then divorce occurs if he intended it and the condition was met, and he must be asked about his intention.