They worked pretty well in the opposite direction. Don't forget that the Lordship was at least as powerful as the Kingdom of the Scots.
The Lords of the Isles were quite able to raid the western seaboard of Scotland. They never however managed to penetrate the heartlands of the realm, whereas the Scottish Crown did on a couple of occasions get to the heart of the Lordship, albeit with some difficulty. In 1411 they did manage to break through to Aberdeenshire, but they were stopped at Harlaw by local levies which hardly suggests that the Lordship was more powerful than the Kingdom of Scots. Indeed the following year the Regent, the Duke of Albany, brought an army into the earldom of Ross, which the Lords of the Isles sought to claim, and forced the then lord to submit to his authority. No Scots king was ever forced to bend the knee to a Lord of the Isles. And in 1475 the King of Scots, James III - by all accounts a weak character - forfeited John of the Isles of the earldom of Ross and made him a Lord of Parliament, which is the lowest rank of the Scottish peerage - would a ruler as powerful as the King of Scots feel obliged to accept such humiliating terms?
In military terms, Scotland was not on a par with the Lordship. In terms of the area under it's control,the Lordship was far bigger than the Scotland of the time.
What proof do you have for the first assertion? The Lords of the Isles might have been better at hit-and-run warfare but they could be and in the end were ground down by a sustained royal campaign. They had no access to artillery, for example, or heavy cavalry. That's the equivalent of saying that the Viet Cong had greater military capacity than the US - yes the former may have been better able to fight in some forms of terrain than the US Army but it's nonsensical to assert that the United States were not at the very least on a par with the Viet Cong or North Vietnam on military terms.
As for the size of territory, while the Lordship of the Isles was large, even at its greatest extent - including the earldom of Ross in the fifteenth century - it did not come close to matching the size of the Kingdom of Scots. And the earldom of Ross was very firmly within the Kingdom of Scots. In fact the Lords of the Isles sought to integrate themselves into the Scottish nobility during the later fourteenth and fifteenth centuries, although eventually without success - they married into the Stewart royal family and sought places on the king's council.
In both cases, it meant the best-protected blood-thirsty thieving bastard around.
That is an oversimplification. In Gaelic terms a king was anyone with control over a large geographical unit - hence why you had Kings of Man and various parts of Ireland. In European terms kings were only the top rank of sovereign rulers. Hence why England, Scotland, France, Castile and so on had kings which were recognised internationally or at least within Christendom. The claim of the Lord of the Isles to kingship was never recognised outside of the Irish seaboard and was in fact effectively dropped by the middle of the fourteenth century.
What this goes to show is that while the Lords of the Isles were very powerful magnates they were not anything like as powerful as the Kings of Scots - they had neither the wealth, the resources, the manpower or the diplomatic recognition.