Well given the fact that the child's guardian will not take responsibility for the damages, I think you either eat the damage yourself or seek a legal remedy.
I would strongly suggest filing a claim in small claims court. It isn't hard to do. You just go down to your county court house and pick up the forms, fill em out and plunk down a small fee in the process about $50.
I did this once against a tenant who skipped out on me and owed some back rent and this was a commercial situation so I could go after the firm involved. They just did not WANT to pay the rent. And they had to cough it up.
Sounds to me that you have a very very similar situation here. I suppose that they could claim that the accident never happened and that you dreamed the whole thing up. But most people can not do a bald faced lie convincingly and I would think the judge would be mighty suspicious of such a "defense". Just have documentation on the damages involved on your bike and possibly a witnessed written statement from the LBS mechanic that the damages on the bike are consistent with your account of the accident.