From reading some Microsoft Support pages, it seems there are two kinds of PINs:
I believe you are currently using the Xbox Profile specific PIN which is tied to your profile, thus it is the same PIN on all consoles:
Your PIN is tied to your Xbox profile so that you can use it with any Xbox console that you sign in to.
But, I think you may be able to use an access PIN instead:
When no one is signed in on your console, you can use a 6-digit access PIN to limit access to content such as inappropriate TV content, games, or apps.
An access PIN is useful when:
- You don’t want younger members in your household using content that’s above their maturity level settings.
- You want to make sure that the sitter doesn’t access inappropriate content.
- You live with roommates who don’t want to sign in to your console when you’re not home.
To create an access PIN, do the following:
- Press the Xbox button to open the guide.
- Select Profile & system > Settings > System > Access restrictions.
- Select Create an access PIN.
- Use your controller to create a 6-digit passcode. Make sure that you use something you’ll remember but that can’t be guessed by others.
- Enter the PIN again to confirm.
By the sounds of it though, anyone accessing the console in this manner won't be signed in to an Xbox Profile, and thus I assume things like achievements and other features won't work:
Note An access PIN is different from a guest account. An access PIN is a reusable passcode that allows guests to use your console without requiring you to sign in to your Microsoft account. A temporary access account can only be created while you’re signed in, and it’s deleted as soon as you or your guest signs out.
...but if you and your children don't mind this, then I believe it should be a viable solution.