Is the marriage valid, and must it be renewed every time the husband returns to a sin he promised Allah to abandon, then returns to it? And is the covenant broken upon its first violation? And is the marriage valid if the wife believes that Jesus, peace be upon him, was crucified?

Your statement "If I return to this sin, then I am a disbeliever" does not render you a disbeliever (kafir), but it is a reprehensible statement that obligates you to repent and offer expiation for an oath (kaffarat yamin (definition)). There is no need to renew the marriage contract.

As for your wife: - If she is a Muslim who believes in the crucifixion of Christ due to her ignorance, then she is not to be judged as a disbeliever, and your marriage to her is valid and does not need to be renewed. - If she is a Christian who believes in that, then your marriage to her is valid, and it is commendable to invite her to Islam. Her mere conviction that Christ was not crucified does not remove her from Christianity unless she fully embraces Islam.