The license.avastlic file that came with the email can be saved to your hard disk (it is also a multi-PC license that you purchased for 3PCs), so you can send a copy to your parents (email or a file store like your dropbox or other file share where they can download it.
They copy it on to there respective PCs and double click the file the avast program will insert it into the program.
If you purchased it using your normal email that is associated with your my.avast.com account, I believe that should be detected in your avast account. If your parents when they registered use your account you might even be able to assign the license to there PC/device.
That assumes that you can see Licenses in your my.avast.com account.
If you need another copy of your license - Resend avast License
https://www.avast.com/resend-license-paid.php, you will need to enter the email that you used when purchasing the license, e.g. the one that the original email with the link was sent.