We'd need a lot more information to even hazard an opinion.  What was
done?  What was negligent?  What did the dentist specifically admit to?
 Was an offer of compensation made?
If both dentists are ADA members and the local dental society has what
is called "peer review" that may be one process to pursue (though it's
closer to arbitration than mediation).  If everyone is talking to each
other it seems some arrangement can be made.
Here we have nothing but heresay.  Why did you leave the first dentist?
 Why did you go back to the first dentist?
It is very risky to make judgment on dentistry that one has not
performed him/herself.  One can say "this crown has an open margin" and
disclose the condition; it's not OK to say "this dentist did a lousy
job" because there can be very plausible reasons why it may not have
been possible to do any better.
Or not.  You probably don't want to get into litigation, and not many
attorneys will far pursue a case of this size (if indeed the damage is
limited to $10,000), so a little open discussion is called for.

Good luck,
Steve