I agree with much of slim's earlier comment. It's certainly premature to claim the idea of a resurgence of the UN (or possibly a successor organisation) is dead just because Trump has been re-elected.
Four years is a short time in world history, and the UN is already nearly 80 years old (even older if you count a continuous line from the previous League of Nations as a model for world governments).
There are a few possible outcomes:
1) Little change. For all the fears of Trump opposers and expectations of Trump supporters, his time as President may not make much difference in the long term. Look back through history - even just since the year 2000 and think of things we thought would be massive world turning points - September 11, 2001, for example - and in fact, on the grand scheme of things, they have changed relatively little. That includes Trump's first term. The world didn't burn down, but nor was there happiness and unicorns for all. The UN is still there, its membership pretty much as it was before (with the same 5 UNSC members). It's still getting involved in world trouble spots but unable to stop wars, and still having its own members killed by fighting nations, armies and groups, with no real comeback or punishment for the offenders. (Not much use for a world-ruling organisation!)
2) Trump acts in a way that weakens the UN, maybe even directly undermining or removing it. Even if this happens, by the end of his term it may just lead to the formation of a new successor organisation - a UN 2.0 if you like. Maybe Trump himself will be responsible for starting it, as a replacement on new terms of reference to the old one.
3) Trump acts in a way - perhaps inadvertently - that strengthens the UN in the long term. It may even be that the way Trump carries out his international politics might strengthen the future of the UN.
a) Positive example: he succeeds in mediating in various conflicts - that would strengthen the UN in the long term, as the thing most likely to break up the UN (apart from direct action against it by the USA) is if the member states are so divided in warfare that they cannot sit round a table. If the world temperature for war is cooled down, then there is more room for the UN to work.
b) Negative example: he fails to resolve the various world conflicts, possibly making them worse - the world would eventually need an organisation like the UN even more after future bloodshed, to bring nations to the table in an attempt to bring "world peace", especially if the US administration is seen to fail badly at peace-brokering alone.