Does the husband's statement to his wife: "I do not want you, rather I want your mother," count as an implied divorce, and is his claim that he did not intend divorce believable when he said "I do not want to speak with you" as an explanation of his intention?

It is clear that the husband does not intend divorce by these words. Even if we assume his words could be considered a kinayah (allusion) for divorce, a kinayah does not effect divorce without the intention, and his statement regarding what he intended is accepted because he knows his intention best. So, the questioner should ease her mind and beware of obsessive thoughts regarding the matter of divorce.