My response is a normal and viable solution for your issue.
Of course it is.
Someone needs to remember or write down the password that they set.
If I set a Facebook password, I need to remember that. When I go and change my Google password, I need to remember the password that I set for Facebook, because it's not going to change automatically when changing Google's password.
Most passwords aren't interlinked, and if you change one manually, you have to either change the other and remember what the other one was.
So that's why you write it down, like I said earlier. It's really that simple.
Again, like I said earlier, write the password down and store it in a secure place. Now you don't have to worry about any of this.
The FileVault password has nothing to do with the AppleID. You can make it the same password or make it a different one. Just like my IMDB password has nothing to do with my MacRumors password, unless I choose to make it the same password and change both at the same time.
Write your family's passwords down.