Lots of things to check!!!!
I haven't worked with Zone Editor, but from screenshots I got basic idea about how to add/modify records for managing zone.
Just to clarify the query here, only below setup is not working:
For e.g. your domain is xyz.com, addon domains are abc.com and jkl.xyz.com.
One external user
ghj@gmail.com sends mail to
tyu@jkl.xyz.com, and if fails by saying "receiptant not found".
Please confirm.
If above is the case, from outside network, check for below things:
dig xyz.com
dig abc.com
dig jkl.xyz.com
dig MX abc.com
dig MX jkl.xyz.com
This will give you Mail server records for those domains. If you are not able to find any records, then you need to add appropriate records in zone editor of Godaddy interface.
Hope this helps!