Wire Transfer is one of my many responsibilities at work so I could probably answer your question.
You and your parents hold accounts at two separate financial institutions, right?
Assuming both banks are located within the US, the FED wire system isn't up on weekends or governement holidays. After your wire has been entered (by internet, phone, mail, fax or in the branch) it usually has to be verified then goes through OFAC (Office of Foreign Asset Control which looks for wires going to Cuba, or Osama Bin Laden, etc.) then it goes through a RISK area to ensure that your parents have sufficient funds in their account to cover all pending transactions including your wire transfer then it goes out to the FED system to receive an 18 digit FED IMAD reference number. Unless your bank does MEMO POSTING you'll probably receive the credit at the end of business Monday, available for withdrawal Tuesday. If you have an account with the big 15 US banks then they probably have MEMO POSTING.
After the wire has been verified & released, passes through the OFAC filter, gets an ok from RISK and gets assigned a FED IMAD ref then it takes about 5 minutes to reach your bank ... how long it takes your bank to credit your account, only they would know.