Is the husband's statement to his wife, "I no longer want you," with the intention of conditioning this 'unwanting' on the continuation of problems, considered a divorce if he did not utter an explicit divorce pronouncement?

The phrase "I don't want you" is an كناية (kinaya - an ambiguous or allusive divorce pronouncement). Divorce does not occur with it unless the husband intends it. Since the husband stated that his intention was that he did not want the problems to continue, and he did not intend to effect a divorce, then no divorce has occurred. This is merely a promise of divorce if the problems persist, and he is not obligated to carry it out.