Could be dealing with anxiety. Could be dealing with attention deficit, Could be dealing with bullying. Could be dealing with a learning disability. Could be dealing with deafness. Could be .... Have her parents seen the child's pediatrician? That might be a wise place to start; at least to rule out the physical components. Perhaps others on this board might be more helpful.
i've worked with many kids like your granddaughter- all typically developing children. jdtm does bring up some things that may be worth looking in to, but in general i find that some kids just have that personality.
honestly, it sounds like you are on the right track- the most important thing is to maintain communication with her teacher so that you can share and compare notes on what may be working. there is no magic trick that will resolve this. you can't change a person's personality- if it is her personality that is causing these behaviors. the best you can do is to help her recognize and manage her urges to tell others what to do.
i'm drawing a blank when thinking of suggestions, especially since each kid is so different. perhaps she needs something concrete, like a checklist, to remind her that she has to listen as well? to strengthen her listening skills, maybe play some listening games. for example, give a series of silly instructions and have her try to remember and follow them. then give her a series of instructions but give your husband or another family member a different series. again, see if she can follow her own instructions without focusing on what the other person is doing.
Maybe a good idea to see she is now asserting herself and finding she has a mind of her own, focus on her good points ,actually it reads like every young child I have ever known, She sounds absolutly Normal, a lot of children 'tune out" and they are people do they have to pay attention all the time ot they get the label of a Disorder.I doubt if a 6year old will be able to be a good listener yet.
A normal 6 yr old only has a short attention span. I doubt that her teacher is unaware of this. So, the teacher's expectations are not too high. A 6 yr old should be able to listen. Her personality shows she wishes to lead and help others. You said even though she doesn't seem to be paying attention that she is able to recall what you said. I have taught many children in the past that can prowl in their desk, play with an object, look out the window, etc. and still answer questions about the instruction taking place in the classroom. Some children are able to multi task while others are not. I would just suggest you keep an eye on this for changes. Children who can do this sometimes frustrate some teachers who don't quite understand what is going on. My theory is if they are getting the instruction, let them prowl in their desk or play w/an object. What is the objective; to have them sit still or have them learn? As far a ADHD, that is easy to check for. All you do is fill out a checklist and the teacher fills one out. Then the dr. decides. Be careful, though. All 6 yr olds have some symptoms of ADHD. The key is to what degree.