Congrats! You have an easy application. If you’ve joined a lineage society within the last year or so, your application meets current standards. As your paperwork is already on file, all your family member will need to do is document where their family line differs from yours. Your parents will not need to provide anything new.
Beware! This does not apply to applications more than a few years old. Application requirements have been changing dramatically over the last decade. What was allowed to be submitted even three years ago is no longer allowed. Your grandmother’s application from 40 years ago almost assuredly no longer meets standards. Expect to need to find the documents needed to bring it up to date.