Unfortunately state primaries often stuggle to allocate sufficient time to the artistic side but in some ways this can be a 'fun' way to spend time out of school - at a local Saturday morning drama class maybe? Does your school have a visiting instrumental teacher ? - we are quite well served in our area with a good local Saturday music school as well.
I dont have any experience of Kumon but haven't heard anything very complementary. Might be worth starting a specific thread to get opinion on the forum?
I agree that you dont need a tutor & as a parent there are lots of educational games & activities you can do to encourage thinking skills etc.
There is a good catalogue/internet site but I'm not allowed to mention names - try a google search?
If your daughter starts to become disallusioned with school work through boredom then a tutor might help her maintain her enthusiasm for academic work, if not for school! I certainly wouldn't advocate ' coaching' - more someone who will encourage her love of learning and make her feel her skills are valued.
I dont approve of young children having over inflated egos because they have been blessed with a good brain but some schools go to the other extreme and bright children can stop working because they dont want to stand out - depending on your daughter's character, one-to-one sessions with a good tutor could help her to appreciate the value of making the most of her talents.
My youngest DS was in mixed age classes for a while & it was fine when he was in the lower year but not in the top year! I think it takes a very good teacher to sufficiently differentiate every lesson for such a wide ability range. It can also be difficult socially because friends move classes at different times. We moved my DS before year 6 but if your DD is bright then I would want to be sure there will be sufficient 'stretch' in year 6.
Most schools would welcome offers of support from parents so its a shame 'communication' isn't great. I have a fair amount of experience of working in schools as well as having 3 children with SLDs and have to say that many teachers have a tendancy to be defensive if they think they are being challenged by a parent - the very best teachers dont!
It sounds like you have tried not to give them this impression at all but I guess because they do have to deal with 'pushy' and 'disgruntled' parents quite a bit teachers can just assume you are being critical.
I never worry about asking very basic questions of teachers - even at the risk of appearing stupid! - or having them explain things in simple terms if they slip into jargon. With some staff this is a skill they develop, similar to politicians
In my experience , as long as you are polite & reasonable the good staff are happy to explain and appreciate all the parental support they can get!
Not knowing what your situation is it may not be possible, but if you were able to offer to help in the school in some way that would benefit all the children - not necessarily in your child's class - it might help demonstrate that you are supportive of the school? If you are good at Art/Music/Drama maybe offer to help with Christmas production in some way? Or a few hours a week helping with Art/Craft in the classroom?
I do hope you manage to sort out communication with the school - I know from experience what a difference it makes!