What should I be required to pay for a shoplifting incident committed by my minor child?

These civil demands are routinely made but rarely, if ever, acted upon.  In other words your chances of being sued are virtually zero.  So you can ignore this letter if you want.  Be aware, if you don't pay after this first letter you will get second, and it will request an even higher amount.  Again, you can choose to ignore it.  If, however, you do decide to make payment, pay no more than $50 (plus the retail value of any merchandise that may have been too damaged for them to re-sell).  I would put this in a letter to them; don't speak with them directly.  These people or notorious for their threatening and intimidating tactics.  
  
If you do choose to pay prior to any court appearance, such a payment will not negatively affect your case.  In fact, maybe the opposite. In these type cases, a prosecutor can ask the court to order restitution.  If you pay the amount requested in the civil demand letter, you should retain proof that the payment was made so that they can prove to the prosecutor that no additional restitution is owed.

If you don't settle the case, they could sue you for the cost of the key chain and possibly for the attorney's fees involved in collecting from you. It's not a guarantee they'd sue, but they could, and at the least, you'd need to defend yourself (note: as a parent, you're civilly, though not criminally, responsible for a minor child's actions).

They are not allowed  to make referring the matter to the police contingent upon receiving a settlement, though in practice, I'm sure stores often do. That is, legally, whether or not they call the police, press charges against your daughter, etc. should not depend on whether they received a settlement, but again, I have little doubt but that this is in fact a consideration.