While I'm not certain that this is the same one that took the mace hit, I'm pretty sure the one that did was not a child of her Reimu. That was the first one, the one at the beginning who thought it was a devastatingly great singer, while really just being devastating. When the clan shunned her and found the badged one (Elegant Lady's pet) and found that she could sing, the original one got jealous and stole the badge, presumably knowing badge = pet = taking it very easy. At least I think that's what's going on.
More or less. The elegant lady loves Reimu's song but Reimu ran away, and the humans were sent to look for her. The jealous reimu heard the conversation between the pet Reimu and dosu and decided to go show off her skills to the humans when they came by.
Also I'm pretty sure this one's the Reimu that got smacked with the mace. No idea how she survived the hit, but I guess it's a happy end.
@Toawa Yes, that was easy to follow. It's that there was the Elegant Lady looking at a picture of two Reimus, which I presume were her pets. But why would she want to lock the younger Reimu up?
Yes, it's easy to follow that the Deibu tried to be get taken back in her place, but whether the Elegant Lady was hunting her original Reimu (the good singer) because she hated it for some reason (hence, the macing), or because the Deibu was such a bad actor that she hit it out of revenge and locked it up?