Economically (not in any particular order):
1. Trump doesn't expect any country to stop trading with China just like he doesn't expect the US to stop trading with China.
2. Trump wants fair trade/trade practices from China and he is using tariffs to enforce it. He expects other countries to not allow China to use them as a way to bypass those tariffs.
3. He wants to protect the USD's status in global trade and reserve currency status. He will also use the threat of tariffs to accomplish that.
Militarily:
1. Trump considers China to be the primary threat.
2. The actions / focus related to Panama Canal, Argentina, Venezuela, Greenland, and Brazil are all related to China. It is to ensure we don't come close to a Cuban missile crisis situation and make sure China cannot project military power at the scale that the US is capable of now. It ensures the US has enough distance between from enemy launch sites to shoot down any missile heading to the continental US states.
3. Russia is probably seen as a future ally against China as opposed to being an enemy. A lot of things make more sense when you consider that as being the ultimate goal.
4. Trump is making every country choose sides now while it still has enough economic influence to ensure they side with the US. If the Democrats had won the White House, and China was allowed to continue as before... without #2 above, it would be a lot more difficult to stop China in another 8 years.