What is the ruling on separating from the second wife after the marriage contract, whether before or after the wedding ceremony, knowing that the reason for the separation is embarrassment from the spread of the news of having met her by phone and the fear of that affecting the children?

Divorce is inherently disliked (makruh (definition)) and should only be resorted to when there is a valid justification. Your apprehensions about how you came to know her and your concerns for the children are not considered justifications for divorce. If she is righteous, then hold onto her and live with her kindly. Childbearing is a shared right of both spouses, and neither should be prevented from it except for a valid excuse.

However, if she has a flaw in her religiosity or character, or if you no longer desire her, then there is no blame upon you in divorcing her. Divorce before consummation is preferable because it causes less harm.