Hi,
From your description, I would like to clarify the following things for troubleshooting:
1. Make sure that you have created a legacy URL to point to the Exchange Server 2010 CAS server.
2. Add the legacy URL in the external DNS zone.
Here is a helpful thread for your reference.
OWA Coexistence 2007 and 2013 (Note: Though it is Exchange 2007 coexistence with 2013, it is also helpful to Exchange 2010 coexistence 2013)
https://social.technet.microsoft.com/Forums/exchange/en-US/bc6fd22a-f653-49a7-a87d-161a57802fef/owa-coexistence-2007-and-2013?forum=exchangesvrdeploy
Hope this can be helpful to you.
Best regards,