I agree they feel different, in my opinion the difference between Bastard and the use of Fucking here is people usually use "Bastard" to punch down at others whereas people usually use "Fucking" as an attempt to punch up at an overwhelming force or entity.

In otherwords, it feels off for Trump to say "Fucking" because it comes off like somebody who has lost it trying to open a door and is now screaming at the door saying "Open this fucking door!" in a tantrum.

It doesn't feel off for Trump to use "Bastard" because it is much more commonly used to assert power by punching down, the entire origin of the word being a label used to punch down at "illegitimate" children.

The established decorum doesn't care about the President looking violent, it cares about the President looking weak by resorting to language "weak" powerless people use.

To the Trump mindset, weakness is guilt.