Eleanor was clearly clever and scheming. That's a matter of record.
No, it isn't--that is a particular interpretation, and a very outdated one at that. I don't think you could find a notable historian of the past 50 years who would agree with it.
Eleanor was a political actor (as befits the heir and ruler of half of the Angevin empire), and she was indeed a shrewd politician and gifted administrator, but not in the way you imply. The idea that she is some sort of devious schemer or instigator is pure fiction (fantastic fiction and drama in
The Lion in Winter, but still false). There was a time (roughly in the early 20th century and before) when historians did characterize her as such (in itself part of a lionization of Henry II), but scholarship has vastly revised that characterization.
You do not need to take my word for it--see Jean Flori's seminal biography on her for a general view and Martin Aurell's books for a dedicated separation of myth and reality. In English historiography, the foremost current biography is probably Ralph Turner's, which is also very good. All of them will confirm what I'm saying here and actively dedicate ink to dismissing these outdated notions.
His total failure to understand anything about Islam suggests the historic Richard weren't too bright. Not to mention his preference for fighting wars rather than the nitty gritty administration of a couple of countries.
Richard was far from the flawless archetype of Robin Hood legend, but your characterization of "total failure" in understanding Islam is simply false. If anything, Richard dealt with Saladin much better than other European princes, sometimes better than local crusading powers, and often much more flexibly and imaginatively than both. This is backed not only by Latin sources, but by Muslim ones as well.
If you read any serious history published in the past 75-50 years, you'll find that the late Victorian perspective of a brainless Richard has long been debunked. You may easily check this by reading the most recent historiography in the subject (Thomas Albridge's works are very accessible). John Gillingham and Jean Flori's biographies on Richard are also very good, remain standards in the field, and probably read better overall. None of them lionize Richard, but none would describe him as dim-witted either. Quite the contrary.
But if Henry II hadn't believed Eleanor's role was significant, and that she remained dangerous, he wouldn't have imprisoned her for the rest of his life.
Eleanor's role
was significant (besides being the key to the better half of his empire, she was the French king's ex-wife and mother to his rebellious children, one of which was forever at large), but she wasn't the instigator. The isn't a shred of reliable evidence to support that claim that isn't easily identifiable propaganda, and she would hardly have the means to do so. A multitude of factors created the scenario that allowed for rebellion, and what finally sparked the inevitable revolt was the Young King being spurned of lands promised at his coronation in favor of the youngest son. After that, many factions with different grievances saw the opportunity to act.
Besides, Eleanor needn't have been dangerous on her own merits for him to imprison her. The mere fact that she was the ruler of Aquitaine justified her imprisonment. This is a reocurring pattern: you imprison the rightful heir to ensure others won't take up arms in their name. The heir didn't need to be competent to pose a threat (often they weren't, imprisoning children was common practice).
For the record, I think it's perfectly fine to portray any historical character in an ahistorical manner in a Robin Hood show. There is a proud tradition of that and I don't think anyone looks at this as an educational tool. If anything, I'm looking forward to see what they do with it.