Thanks for the additional background info moomin, that makes a difference in what I have to add in my response and I hope you weren't offended by anything I said in my response, not being aware of your background.
That said, I still think it's a good idea to seek out a private evaluation. I can understand the difficulty with going through the school and the concerns you have. A private evaluation comes with no hidden agenda, and you will have the opportunity to ask more detailed questions as well as get referrals (if needed) to private providers and/or recommendations for school.
My gut feeling is that if your dd is struggling in more than one setting (swimming lessons as well as what I think you have listed as more than one preschool setting) it's a good idea to have someone who is a professional look at what's up - no matter how incredibly well she might be doing at home and when she's focused. I have found with my own children that it's easy to compensate at home without realizing it, and home is also a very familiar place for our kids, so it can be a place where a child who is stressed out in the outside world can feel relaxed and happy and not appear to be struggling - yet that anxiety or whatever is there is still a part of what's there in your child, and jmo, but I'd want to know what's going on and find some help for my child to learn to navigate those other situations.
It might all be simply nothing more than gifted quirks, but I'd want someone other than just me evaluating and reassuring me that is all that it is.
Best wishes,
polarbear
