Hula, does she actually get a choice or is it guided?
At our school, all the Y2 children are trialled on all instruments (from Y3 we offer cornet, trombone, french horn, viola, violin, oboe, clarinet, cello). They spend an afternoon, blowing, bowing and plucking and each peripatetic music teacher grades them A* - C on their specialist instrument.
The music co-ordinator takes into the scores given by the peris, along with their ability on recorder, their academic ability, their musical ability (form her observations of the class music lessons she teaches each week) and whether they play an other instrument already. She would not normally give someone who plays piano the viola, as it's yet another clef to learn.
There are a limited number of places available for each instrument and sometimes thechildren don't get their first choice, because no matter how much they liked it, they couldn't actually do what itshould do with it!
Bassoon, sax, classical guitar, percussion and voice are offered in later years (Y4/5/6).
DD played piano from 5yo and dropped it at about 9/10yo iirc, having reached Grade 3. She took up sax in Y6 and got Grade 4 in March (Y7). She has played violin since Y3, just about to take Grade 4 and played that in a local youth orchestra (training) and then swapped to viola for orchestra and kept violin at school. The viola helped a bit with her Grade 5 theory (passed in March). She can also play the cello a little (altho not recommended for a violin player because of bow technique, like shouldn't play clarinet and french horn for example) and has tried out a friend's harp.
Anyway what I'm trying to say is it might be useful to get some very good professional advice. DD's relationship with the violin is strongest, even though she frequently finds it challenging and it was chosen for her through the school system I mentioned when she actually wanted to play the trombone!