No, you cannot file your children's extensions from your own account.
You have to create a new account for them and
report their information under the new account.
See
instructions
1.
Sign
out of
TurboTax Online.
2.
Select
the TurboTax Online product you
want to use for the second return and proceed.
3.
On
the Create your account screen, set up a new login for the
second return.
o You can reuse your email address if
you want to receive e-file notifications for the second return.
o Up to 5 accounts can be tied to the
same email address.
4.
After
you've created the new account, you can start working on the second return.
Tip: If you're
preparing multiple returns for family members, it's more economical to switch
to the TurboTax CD/Download software, which lets you e-file up to 5 federal
returns at no additional cost. More
info