The 2nd American War of Independence is a war between 
USA and 
United Kingdom. It happens if the United Kingdom attacks the USA with an 'acquire state' or 'conquest' casus belli.
If that scenario happens multiple times, it will be called the 3rd American War of Independence, 4th American War of Independence, and so forth.
It is, however, very unlikely that the independence of the USA will ever challenged by these wars.