Can a wife who has betrayed her husband by phone be trusted with raising the children, especially since the husband is not certain of the sincerity of her repentance and there are indications of her psychological instability?

If the wife divorces herself due to her immorality, it is not advisable to return her to the marital home, because immorality is a legal impediment to custody. It is proper to divorce an unchaste wife who neglects the rights of Allah, and whose husband does not feel safe from her corrupting his bed. The husband is permitted to make things difficult for her until she ransoms herself through khul', based on the verse: {And do not constrain them to take away part of what you gave them, unless they commit a clear immorality.} However, if the wife repents sincerely, returning her is more preferable to preserve the family and children.