I suppose that you could argue that the two conflicts are similar. You could say that they both involve one side trying to control and dominate while the other side tries to break free.
In the story, Dame van Winkle is a very domineering wife. She tries to impose her will on her husband as much as possible. Rip wants to get out from under her influence and live life as he pleases.
This is similar to the conflict between the colonies and the British. The motivations are different (Rip is motivated by laziness as much as anything) but the basic desire is the same. The Americans want to be left alone to live their own lives (as a country) without being dominated by England (the way Rip's wife dominates him).
I guess if you take it a step further you can see another parallel (if you choose to). You can argue that both the British and Dame van Winkle have a good reason to be angry. The British (you can argue) have a right to expect the Americans to pay taxes and obey the laws. Dame van Winkle has a right to expect Rip to be a bit more conscientious and hard-working.
So you can say that the British and Dame van Winkle have a reason to be mad, but that that the Americans and Rip also have a reason to want their freedom. In these two ways, the relationships are similar.