I, too, was told to go sit in the library, but I finally just started going to the assembly and not telling my parents. They objected to the flag salute when the thing began, it was sometimes oriented around a holiday, or they would have us build up school spirit for a football game, or just sing "objectionable" songs. The elders advised to not put the kids in a group situation where peer pressure might weaken them, and they join in the flag salute or national anthem, or similar wicked acts.
Children and school assembly
Since you are in the UK, things are different there.
Here in the states, when I was growing up... I think that I was the only JW going to the school I was in. (If I wasn't, I didn't know of any others - as they were quiet)
There were certain 'assemblies' that I wasn't allowed to attend - mainly holiday-related (Christmas, Easter, etc.). There were others too... like around Fiesta, there was a 'King Antonio' - which is a locally 'crowned' man - usually well-known in the area - who supposedly presides over the week-long event. (He mainly rides around in parades and tosses candy to the on-lookers).
I remember not getting to go to that one... every other kiddo got a trinket - but not me. The halls of the school were quiet that day, as I was the only one not at the assembly.
When I got older, and in the upper grades, there were the pep rallies - for the school football teams... I was allowed to go to them... but couldn't 'participate' or stand for the pledge, etc. Stuck out like a sore thumb then, too.
Anyway... I think that it has more of a psychological effect on younguns when you single them out - and isolate them from gatherings - not allowing them to go. It also makes them 'targets' for the bullies in the schools.
This also raises an issue which I have long held on "home schooling". It has the effect of isolating kids from normal society and facing the facts that many other people have widely different viewpoints to what their parents may want them to have. Such kids are sure to be looked upon as weird and different if they are ever fortunate enough to make it to higher education later in life. Same with hiding from a school assembly.
I think that this kind of isolation and "marking" of JW kids to be weird and different causes great psychological harm. Kids already have enough emotional baggage to grow out of without the parents "dressing them funny", so to speak. Obviously, part of the purpose of public schools is for kids to get a feeling for the real cross section of society; even if part of the curriculum may not be what they personally hold.
So - if these kids are so well indoctrinated at the Kingdom Hall, what the hell are the parents afraid they might hear at a basketball pep rally?
i remember mine...it was in the days when all pupils gathered daily for a service to start the day even though it was not a religious school...anyway my sister had started the same school the previous year and my parents had informed the school that she would not be attending the daily service..not a problem..except for some reason they assumed that because i was the same surname the school would make the connection that i wasnt to go into service...but they didnt and so i found myself right at the front of the hall on my first day not even 5 years old in my new blazer and short trousers with all the other pupils behind me knowing i shouldnt be there..so i started crying..and first my teacher came to see what was wrong but quickly got frustrated because i couldnt explain myself..so she smacked me for crying and kept smacking me to get me to stop crying and then got the headmistress to smack me to get me to stop crying until eventually time was up and they had to cancel the service.....result...still loved school though...tijkmo