The EU and the UN are completely different concepts.
The United Nations is merely a supranational organisation. The EU is a de facto country, with its own citizenship, passports, visa regulations, flag, anthem, government, parliament, currency, central bank, etc.
The UN or the former League of Nations had none of these (well, yes a flag, and that's it).
Trade within the EU is much more important than between the EU and USA.The UK is an example. Trade coming from the USA into the rest of Europe usually comes via the UK (not always physically, but over UK markets etc) and so money comes into UK. If the USA fell out with all of Europe, the UK could collapse into Economic depression, and so could the rest of Europe and the USA. The main of the money in the UK comes in some way from Trade and exporting etc.
The USA represents only 24% of European good exports and 14% of good imports. Over half of the trade in Europe is done within the EU. (Sources)
I don't know where you got the idea that "trade coming from the USA into the rest of Europe usually comes via the UK". This is just not true. The UK might be the biggest European importer of American goods, but in 2005, out of the €162 billion of goods imported from the USA into the EU, only €34 billion were imported via the UK (21% of the total). Proportionally the Netherlands imports 3x more (€22 billion for a population 4x smaller).
What is more, the EU economy is bigger than the American one, and the EU exports more to the US (€251 billion in 2005) than it imports (€162 billion in 2005). Greece, Cyprus, Spain, the Netherlands and Luxembourg are the only European countries that import more from the US than they export to the US.
The EU economy also proved more stable to international upheavals than the US economy, as the plunging US$ since the Iraq war has demonstrated.