Assuming that all the routes and database.yml are configured properly the issue may be because of namespace error. Rails see the same name and is calling the teacher controller. So the best way to solve is get the nested application controller code in the single application controller and name the nested controller as something like Childrenteachers controller. Then use something like

class childrenteacher::ApplicationController < children::ActionController::Base

This will be neater and easy for rails to understand.

Easiest solution for this is to use gems to connect to different databases. Refer https://github.com/cherring/connection_ninja for more information. This can be done using this gem. I feel instead of trying as it is mentioned in question, one can use the gem (in the link) and try to use the data in show page. This gem is generally used to connect two databases from two different database servers inside single application.