I’m really scared by that “nightmare scenario” of a Europe that could (1) leave NATO (2) position itself as a military rival to the U.S. that’s willing to use force against the U.S. (3) raise defense spending enough to credibly defend itself from the U.S. and/or (4) stop a military overflight on a bombing run. The odds of Trump not acting like an asshole for the rest of his term is far lower than your hypothetical.
1) It would be NATO leaving the US
2) Since Trump proves that the US can become an enemy it's prudent to prepare for the possibility of US hostility but nukes aren't meant to start a war. Instead, they provide leverage to modify the behaviors of others. MAD comes to mind.
3) Why on earth would the EU need a multitrillion-dollar war machine? A tiny fraction of that amount is all that's necessary as it costs far more to dominate the world than to achieve a deadly retaliatory capability.
4) Stopping a military overflight? So you believe that the US is a material threat to the global community then. We're as bad as your "nightmare" is, eh? If the US tried that then you are turning what seems irrelevant, the rest of the world, to unite seriously against us. How clever that would be. Now perhaps you believe Trump would bomb Europe and he might, but there are ways for a sophisticated technological society to make their airspace virtually useless. Upon US aggression then domestic flights land and full measures taken that makes flight unsafe. No shooting down necessary, just jam communications and nav.
The "NIghtmare" exists already and heaven help us if his taxes are lawfully obtained, eh?