Can Roman Catholic married men become priests if their wives consent?

Answer 1

No, not at all.

A married man can be ordained a permanent deacon with his wife's consent but not a priest.

Roman Catholic AnswerIn the Roman Catholic Church, there are different rites or "Churches", of which the Latin Rite is the largest, and most well known. Following the Schism of the East in the 12th century, most of the Eastern Rites broke into two, thus there is a Greek Orthodox Church and a Greek Uniate Church. Another ancient rite of the Church is the Maronite Rite which uses the St. James Liturgy. Each Church has its own set of canon law, and its own liturgy, all of which are ancient. Only in the Latin Rite and unmarried man normally ordained. Historically, other rites have ordained married men to the priesthood, and this was considered normal. Bishops were mostly chosen form the monks or celibate clergy so they were never married.

So to answer your question, yes, Roman Catholic men who are married may be ordained with their wive's consent, except Latin Rite men. There are exceptions even to that rule, as with the conversions of the Anglian clergy, who may be ordained to the priesthood if they are married, and Rome accepts them.