I don't think you can really say affirmatively that there should only be one process, because there are a myriad of sexual sins a priest could be wrapped up in. A priest was sleeping with another consenting adult? A priest on a gay dating app? These should be handled differently than a priest harming children, obviously, as the latter should be thrown in jail for the rest of his life and stripped of everything connecting him to the priesthood.

In my opinion, priests who scandalize the laity in any fashion (truly scandalize, not just say something stupid about politics) if they are to continue as priests, should be no longer available to the public. This may seem harsh, but if you went through all of seminary and every bit of training as a priest, personal experiences in prayer with God, and you didn't understand your responsibility to the Church and to the faithful? That's not right. Dangerous, even.