Did a divorce occur due to the husband's statement to his wife's mother, "Her mother can come and take her tomorrow," or his statement to his wife, "Let's separate, or each of us goes our own way," given that there was no intention of divorce in any of these cases?

The divorce does not take effect based on what you have uttered in the mentioned instances, due to doubt in the utterance of some of them, the absence of intention of divorce in the allusive phrases, the lack of intent of divorce in some others, and some of them being merely self-talk.