I get the sense that certain kings, like Henry II, viewed England as sort of a backwater and source of ready funds to support their "real" domains in Aquitaine. Is this just my understanding or is there some truth to it?
There may be some truth in that... For example, it was English taxes that largely paid for Richard I's Holy Land adventure, as well as his later ransom. However, due to the turmoil of the Stephen/Matilda conflict the revenues from England fluctuated quite a bit during the 12th century.
Moreover, the Aquitaine was an extremely rich and valuable territory, and the other Angevin lands in modern-day France weren't bad either. I was always given to understand that the kingship of England was just as valuable for the title itself as for the financial benefits - simply to be the king of somewhere. One of the issues with their lands in France was that, while the actual Kingdom of France was weak and tiny compared to the Duchies of Normandy, Brittany, and Aquitaine, they were still feudal vassals of the King of France. As Kings of England, the Plantagenets had an equal claim not only to power and wealth, but also to dignity and status.