Some of these are questionable: 1) The American War of Independence ran from 1776 to 1783. Did the newly created US and its bitter enemy, Britain become instant friends immediately following the war? If so, how do you explain the War of 1812. 2) I'm pretty sure that the relationship between the US and Germany was less than cordial during the Nazi occupation (1933- 1945) and 3) Likewise, I would say that our diplomatic relationship with Mexico suffered somewhat during the Mexican-American War (1846-1848).
Admittedly, I do agree with some of your points but I am following what Wikipedia says to be the date that formal relations began. Over centuries of years, you shouldn't expect to consistently be on good terms! Have you ever had a friend who has never let you down? People always fall out but they reconcile in the end and this is the same situation here.
Britain wanted to resume friendship with the USA because it was a wealth of trade. It needed to trade with us and France and Britain fought over who would trade with USA