Should the colonists be willing to accept representation in parliament? would britain have given the representation?

No, they shouldn't have accepted: the Colonists tried to have appropriate representation, with the creation of the Committees of Correspondence, but even the proposals that the Colonists sent to the British, were not accepted by Great Britain, so to have a place in Parliament probably would not have been accepted by British politicians, or in a few years would have lost that place, or not having a majority vote or representation, it would have been useless and the colonists would have suffered the same abuses by British crown. But it's very unlikely that the British would even have agreed to give them a place in Parliament.

The answer is installation.