I could be wrong but i believe that the reason why the enemy (the mist ninja) wanted rin/rin's body could be because she might of had some sort of unique ability that the enemy were after kind of like when hidden cloud ninja i think kidnapped or tried to kidnap kushina probably cause she had unique abilities and also when ninja from the hidden cloud tried to kidnapp hinata so they could steal her byakugan/learn the secrets about the byakugan.