You can only have one copy of Diablo 2 per Battlenet account. If you wish to have your children play you can do that though. To buy D2 2000 or LoD 2001 for them you can buy it as a gift. Click the Gift button and you can have Blizz send it via email to them or you can have the email sent to you instead and you personally set it all up for them.
Ideally you want to set up a second Bnet account in your name for each minor child. That requires a separate email address for each account. You can also set up Parental Controls to prevent digital purchases, control play time, get play time logs, and even control chat options for modern games.
Now that they have their own Bnet account in the parent’s name you are set until they are 18 at which time you contact Blizz and have it transferred to their name.