I was taught, when I was going to be placed in charge of others, that when it comes to discipline, you praise in front of others and chastise in private.If the AG has a problem with the president...tell him to his face in private. Don't allow a journalist to interview you so you can trash the man in public.
That's the way its always been done in the past.
I'm still pissed about the way he refused to indict Comey for his obvious perjury and LEAKING classified communications.
Now he goes out of his way to castigated Trump in public for a GD tweet.
In this case, AG Barr is the subordinate to Trump and as such, his proper action would be to request to speak to his superior in private and address his concerns.
With regards to Trump, Trump needs to be a bit more professional and presidential in his demeanor (that doesn't mean he can't attack his opponents, just show a bit more...class).