You are probably correct. But King George was not willing to use all the resources at his disposal to prosecute the rebellion in the Colonies. President Lincoln was willing to use all the resources at his disposal to prosecute the rebellion he was faced with.
Fixed it.
Not entirely true. George probably did want to use all available resources to subdue the colonies but he couldnt. We Americans dont like to admit this, but we won in large part because the Revolutionary War transformed from a war of rebellion to a great power conflict after Saratoga.
George was much more concerned with defending Englands posessions in India and the Caribbean from French incursion than he was with the rebellion in America. According to the prevailing economic theories that led to mercantilism, colonies that provided raw materials unavailable to the mother country were far more valuable than colonies that were developing an industrial and commercial base, like the American colonies, especially the ones in the North.
Its no coincidence that British strategy in America shifted to fighting in the Carolinas and Virginia after the French got involved they had already written off New England as lost and would likely have been willing to give up on New York, New Jersey and Pennsylvania as well. Obviously it would have been desirable to hold all of it, but the South, the Caribbean and India were much more valuable.
See my post above. George had his hand forced by France. Had England recognized the Confederacy and formed an alliance, he too would have been forced to divert resources away from fighting the rebellion, just like George was.