Why do you think the Dutch colonists agreed to become part of an English colony?

Are you talking about New Amsterdam surrendering to the British with no conflict and the name being changed to New York?

The reason for that is that the Dutch were merchants. They cared about making money and war would have disturbed their businesses. The Dutch merchants that ran new Amsterdam didn't speak for the Dutch government but the made the decision never the less.

Additionally, Britain was pretty strong and they probably would have lost anyway.