Is the husband's cohabitation with his wife for 14 years and their being blessed with five children, after his saying to her: "If you dye your hair, then you are divorced," considered as taking her back, or does taking her back require the testimony of witnesses, knowing that he never left her except for travels not exceeding a month in most cases?

The woman is still under your marital bond. Your statement to your wife, "If you dye your hair, then you are divorced," is a conditional divorce that takes effect upon the fulfillment of the condition, according to the majority of scholars. According to Sheikh Al-Islam Ibn Taymiyyah, it requires an expiation for breaking an oath. If the divorce occurs, it is a revocable divorce, and you can take her back as long as she is within her waiting period (iddah (definition)), either by engaging in intercourse with the intention of reconciliation or without such intention. The validity of the reconciliation does not depend on the wife's consent or knowledge. The second conditional statement did not take effect because its condition was not met. Having witnesses for the reconciliation is recommended but not a condition. Therefore, she is lawfully your wife, and she must return to the marital home. Her father is not permitted to prevent her.