I can't write about all the Founders' descendants, and I'm not sure if there is a concise source that does write about all of them, but I can at least talk about the Lee family.

Robert E. Lee was the son of "Light Horse" Harry Lee who was a minor Patriot, in that he didn't sign any of the country's founding documents, but he was an officer in George Washington's Continental Army, and served as Governor of Virginia and later as a representative in the U.S. House after the Revolution. I won't go into Robert E. Lee's thoughts on the war, since I'll take it for granted that most people already know--but suffice it to say, after some personal struggle with the question of the war, he decided to resign his commission in the U.S. Army and lead the Army of Northern Virginia on behalf of the Confederate cause.

Less written about is what his what his wife thought about the war. Mary Anna Custis Lee was the great-granddaughter of Martha Washington through her first husband, and as you said, the step-great-granddaughter of George Washington. Historian Mary Brown Pryor gives an account of Mary's thoughts on the war at its outset in her article "Thou Knowest Not the Time of Thy Visitation" published in the Virginia Magazine of History and Biography. The only firsthand account of Robert E. Lee breaking the news to his family that he had resigned from the U.S. Army in preparation for joining up with the Confederate cause comes from Mary and Robert's oldest daughter Mary Custis Lee (the same name as her mother). She made her account in a letter to a potential biographer of her father in the 1870s, though that biography was never written. As Pryor writes:

"[W]hat is particularly striking about Mary Custis Lee’s letter is that Robert E. Lee’s innermost circle was bewildered by his decision. After sending his resignation letter, he did not immediately tell his wife and children but waited until the visitors to Arlington became so numerous that he had to explain his position. And when he did so, calling the family into his office, he apologized, saying, “I suppose you all think I have done very wrong.” The little group was literally struck dumb, because, as Lee’s daughter tells us, “we were traditionally, my mother especially, a conservative, or ‘Union’ family, I, myself, being the nearest approach to ‘Secesh,’ & living in the country, out of the way of the exciting influences that were agitating the rest of the South, & under the shadow, as it were, of the Capitol dome at ‘Washington’ we had scarcely kept progress with the spirit of the times.” Mary finally found her voice and told her father that she did not think he had done wrong, but, according to her account, the others remained silent."

It can be inferred, then, from daughter Mary's account that, had Robert consulted with his wife about his decision before he made it, she would have tried to talk him out of it, which is why he didn't consult with her. She was conservative, but she was pro-Union. Of course, once the decision was made, she stood by her husband.

As Pryor also writes in her article, Robert E. Lee's decision wasn't particularly popular with West Point graduates from the South who still remained in the Army in 1861, nor with U.S. Army officers from the South in general. Southern military officers were split; many stayed with the Union, while many defected as Robert E. Lee did. This point is driven home by Lee's extended family: Robert's older brother Sydney Smith Lee became a Confederate naval officer, but "with great reluctance":

"He serv[ed] without enthusiasm, and as late as September 1863 still "pitched into" those responsible for "getting us into this snarl."

Robert's brother-in-law Louis Marshall, married to his sister Anne, stayed loyal to the U.S. Army and "[n]o one in that family ever spoke to [Robert E.] Lee again".

Probably most famously among the Lee family is the case of Robert's cousin Samuel Phillips Lee. Samuel Phillips Lee's grandfather was Richard Henry Lee, who had been a delegate to the Second Continental Congress, and it was his motion, the "Lee Resolution", to declare independence from Great Britain that resulted in the Declaration of Independence. Richard Henry Lee would go on to serve as President of Congress during part of the Articles of Confederation period, and, later, a U.S. Senator from Virginia after the adoption of the U.S. Constitution.

His grandson, Samuel Philips Lee, a naval officer, did not defect from the U.S. Navy, remaining loyal throughout the Civil War, serving as a Rear Admiral in the New Orleans campaign. But he is perhaps most famous for his response to his cousin Robert's position that he reluctantly resigned to join up with the Confederates because he could not turn his back on his native Virginia. Said Samuel Philips Lee:

"When I find the word Virginia in my commission I will join the Confederacy."

Thus, among the descendants of Revolution patriots Martha Washington (wife of Continental Army General George Washington), "Light Horse" Harry Lee (Continental Army officer and later Governor of Virginia), and Richard Henry Lee (Continental Congressman and later U.S. Senator), their loyalties were split on the war.

As for how they were perceived--as political tools or not--I know of no direct quotes on the subject, but given that Robert E. Lee, his brother Smith Lee, his brother-in-law Louis Marshall, and his cousin Samuel Phillips Lee, all fought in the war, and his wife Mary Custis Lee offered active support of her husband and the Confederate cause, it would seem that they saw their role as more than political pawns. Aside for Robert's wife, they were active military participants on one side of the war or the other.

For other descendants of founding fathers, maybe someone else can offer more information.

EDIT: Fixed link. And one more: George Washington's great-grandnephew John Augustine Washington III was the owner of Mount Vernon at the time the Civil War broke out. He was the great-grandson of George Washington's younger brother John, and so this made John Augustine Washington III the third cousin of Robert E. Lee's wife Mary.

John Augustine Washington III wasn't a military man, but he joined the Confederacy and became aide-de-camp to his distant cousin Robert E. Lee. On his opinion of the Union, this Washington would write in July 1861:

"[T]he Yankees are for the most part a set of plundering fellows, who will steal and bully when they can and do as little fighting as possible."

He was killed not long after, in September 1861, at the Battle of Cheat Mountain. He had a brother, Richard "Dick" Washington, who was discharged from the Confederacy not long after due to poor health, but was taken prisoner by the Union later on, and then released after that in a prisoner exchange. He was advised against rejoining the fight after that, and he did not.

These were the most closely-related Washingtons to George Washington to actually have the Washington surname at the time of the Civil War, but the connection wasn't direct, and their direct ancestor (George's brother John) was only a minor Patriot who did not fight in the Revolution. Considering this, and considering that John Augustine Washington III had no military background yet was given the plum aide-de-camp assignment, these Washingtons could be considered more political pawns or "tools of propaganda" more than any of the other aforementioned descendants of the Washingtons and Lees.