My baby sitter abruptly quit on us after being prepaid in cash , is it worth it to file a claim against her?

Only you can determine if it is worth it to file the claim.  How much does she owe?  Can she pay it if you get a judgment?  How likely are you to win (her written acknowledgement that she owes you two weeks suggests a good chance of winning that part of the claim, less likelihood of winning the third week) Can your claim be heard in small claims court, which generally has streamlined procedures and is less expensive and time consuming than a litigation in a court of general jurisdiction?  What is the filing fee for filing a case?  Will you have to pay a process server and, if so, how much?  Do you have the time to go to court?  Can you handle the case yourself, or will you have to engage a lawyer?  Did you handle everything correctly regarding her employment (there may be tax obligations, i.e. withholding, that you might have had to comply with depending on the terms of your babysitter's employment, and the fact that you paid her in cash suggests that you may not have complied with them)?  These are some of the questions you should ask yourself before determining whether it is worth it to you to litigate.