I am always highly suspicious of "motivation" issues. No child instinctively prefers to do badly. We are almost all born with a desire to succeed, to feel good about ourselves and proud of what we do, and to make the adults around us proud, too. When a child "chooses" to fail, it usually means there is a problem for them with the alternative. The challenge, of course, is figuring out what that problem is.
Telling the difference between "won't" and "can't" is extremely hard. Especially as kids get older, and unrecognized issues compound and have more complex and diffuse effect on seemingly unrelated behaviours. However, if you step back and make an assumption that it really is "can't", and then stay with that assumption for a while and hunt hard for possible barriers, it's amazing what you may find. I find I need to let go of the discipline/ behaviour lens before I can really work with my kids to figure out "why are you struggling with this seemingly simple task? What skills/ resources/ support/ time do you need that you do not have?" And I learn a lot. There's almost always a hole between what what they are being asked to do, and what they believe they are capable of doing. Sometimes the hole is due to anxiety or missing social skills, sometimes it's LD (usually all of the above mix together). Sometimes it's meaningless repetitive rote-work that sends the ADHD into hyperdrive. Always, the hole makes the task difficult, and sometimes it makes the task seem impossible.
As others have noted, the critical question with twice-exceptional children is not whether they can do the task, but whether it just seems much *harder* than it should. They can usually - through super-human efforts and perhaps the right alignment of the stars - pull it off at least occasionally. But they can't sustain it. They may not be able to control it. And when simple tasks, like writing, don't become automated, they are using all their brain resources and working memory simply to produce the letters, crowding out their ability to think about spelling and what word is next, let alone more complex questions like what they want to write, or what the teacher is asking at the same time.
