Yes, hellymelly. My ds1 is also exceptionally bright, was exceptionally anxious at school for reception and year 1 and also rolled his eyes, grimaced and had various other tics. The tics didn't bother me, tbh, albeit they are obviously worse the more stressed you are, because that sort of thing has happened to other members of the family in childhood and isn't an issue for them as grown ups (and was only really a minor issue in childhood). By the way, apart from one little boy in reception who commented on it, no other child ever seemed to tease him or pick him up on it. It was very embarrassing to watch in class assemblies, though, albeit I reminded myself everyone else was focusing on their child, not mine!
The school was fantastic - he had several one-one sessions with a teacher with whom he rapidly felt relaxed and that helped with the anxiety. What helped most, though, was that in Year 2, he now has a special friend, so feels more liked at school, and his brother is at the school with him and plays with him at playtime, and the work is now more interesting (albeit the school is concerned that they are unable to stretch him, because his anxieties make it quite difficult). His tics are really quite subtle, now (I don't notice anything at the moment, except for an annoying little hum he tends to make when he's listening to me reading to him!!!). He is now a really happy little boy and I think that is a lot more important than the difficulty of his work at this stage in his life. I am glad I didn't take him out of school, now, as he has turned a corner, but he was a sad, almost depressed child in year 1, who only felt safe with his teacher.
In ds1's case, the school was so aware of the disparity between his obvious intelligence and his attitude in the classroom and ability to get on with his work, that we did end up seeing a psychologist, who confirmed he is extremely intellectually gifted, but has problems with empathy - he understands facial expressions, is hugely imaginative and thoughtful, but doesn't really understand WHY other children react to him in the way that they do, so finds it difficult to make friends, even though I'm sure he does share some interests with the other children (I don't think liking "Beast Quest" books, playing spy games, making up mad stories and joking about bottoms is that unusual for a 6-year old!). His intelligence makes him acutely aware of his difficulty (he also has a connective tissue disorder, which doesn't help his confidence), but is also I think, a way out of the problem - he can learn to understand what other children find comes naturally (and in the meantime, maths and English come naturally to him, so he doesn't need to work quite so hard at those for the time being!!!). Ds1 has just received a diagnosis of aspergers syndrome, but a child can have an awful lot of these types of difficulties without this meriting a diagnosis (in other words, you don't need to have aspergers to have similar hang-ups!).
ps making ds1 feel totally secure and loved at home really helped, so I think you are doing the right thing, and definitely worth trying to get your dd back into school next year, when she'll have the support of her sister, if not before.