Is this marriage valid and legitimate despite lacking the condition of credibility, and if so, what is the legitimate advice for dealing with this complex situation? Is this considered a trial, and is it forbidden to administer a Hadd punishment by hand?

The marriage contract is not invalidated if the wife deceives her husband regarding her virginity. The husband does not have the right to impose a hadd punishment on his wife or her father, as hudud punishments are entrusted to the ruler. The husband is advised to retain his wife, treat her kindly, and conceal her past, especially if they have a child. His patience in enduring this trial will bring immense reward, and its outcome will be success.