Custom login -> admin
It seems like you would like for one login to give access to Drupal site administrative functionality, and also give access to specialist non-Drupal functionality.

The easiest and most flexible way to achieve this is might be to add an extra link to the Drupal administrative menu. When someone logs in, that new link would be there prominently along side the other Drupal administrative links.

The link could point to another website, to non-Drupal pages and scripts on the same server, or to Drupal pages generated by a custom Drupal module you created.

Perhaps the biggest advantage of putting your custom code inside a custom Drupal module would be that you could use Drupal's access control system: logging into Drupal with the right role would automatically grant users (and only these users) access to your custom functionality.

Generally speaking, taking existing code and turning it into a Drupal module so that it outputs it results "through" Drupal in a minimal but viable way should be easy. 

Fully converting your code to take advantages of all Drupal's API features (theming, UI widgets, etc., etc.) would be a much bigger task. It's not necessary for your stated goal, it's more something you might consider for the sake of improving the robustness of your code by leveraging the quality of Drupal's APIs.