Can a husband take his wife back after divorcing her once on her behalf, and other times by intention, and once by saying "Go to your family's house" without the intention of divorce, then divorcing her while she is menstruating with insistence and after the waiting period has passed in her family's house?

In what you mentioned, there are two clear, effective divorces: the first and the last. The fact that the second occurred during menstruation does not affect its validity according to the majority of scholars. As for what you mentioned to your mother, if it was an explicit statement of divorce, then it is effective, even if the wife was unaware. If it was merely an intention or a promise, then it is not effective. The other instances of divorce you mentioned are merely intentions, thoughts, and allusions (kinayah) which do not constitute divorce unless there was an intention to effect it. If the divorce you mentioned to your mother was effective, then your wife has become irrevocably divorced from you (baynunah kubra), and she is not lawful for you until she marries another husband. If it was not effective, then you still have one divorce remaining. Since her waiting period (iddah) has expired, it is not permissible to take her back except with a new marriage contract. Her spending the iddah in her father's house does not affect the ruling of the divorce, but the obligation was for her to spend it in her husband's house. We advise consulting with Sharia courts or Islamic centers.