Are you suggesting they are not?
So while it's the biggest trade partner, it's not the end all and be all. It's about as important as what the UK was to Ireland before Brexit. Stopping trade isn't helpful, but it's not a showstopper either.
Prior to the First World War there was a view that economical interests would prevent war as well. http://blogs.reuters.com/anatole-kaletsky/2014/06/27/world-w...
Often the ability to sell is motivated by more than just economics.