The answer
If you confess to a different priest every time, you might fall in the thought of repeating the same sin relying on the fact that you will confess, and get absolved every time. Your second point is right; we should abstain from sinning out of love for God, not embarrassment. Will you be honest with the other priest and tell him how many times you have repeated the same sin? Also, staying with one priest will help you overcome, and conquer sin. The priest will give you spiritual exercises, and guide you through the path to get rid of such a sin.As you know, the priest observes complete confidentiality and will pray to God that He may forgive, and forget your sins; the priest will never judge you.
Your priest is your confessor father and as the person has one biological father, he should have one spiritual father. Your priest is your physician and it is preferred to go to the same physician for follow up.
So to confess to more than one priest is not a question of whether it is a sin or not, it is a question of why we have been instructed to have one confessor father.
You can read more about the sacrament of confession, and repentance in the following link, an article by His Grace Bishop Mettaous, Abbot of El-SYRIAN Monastery http://www.copticchurch.net/topics/thecopticchurch/sacraments/.
Answered by His Eminence Metropolitan Youssef (opens in a new tab)