AxCrypt is a file encryption software. AxCrypt 2 now use a single sign on model where the same password is used to sign in to our servers and to protect your files. Sorry to say, It does not support a specific password(s) for specific file(s) feature due to some security reasons.
I will suggest to use two different AxCrypt accounts to achieve the same where one is for your personal use and another is for your family.
We can switch between AxCrypt accounts by clearing the local app cache in the AxCrypt app. To do the same just navigating to the AxCrypt app menu options(File | Options | Clear All Settings & Restart) or click the Reset button in the AxCrypt app sign in dialog.