Hello,
In the first instance, I don't think having the web-app and the primary WP install share the same database should be a problem, as long as the table structures are different as mentioned by you.
However, I'll be happy to discuss this further with you and if necessary, can split the database so as to have a separate/dedicated database for the app.
Please PM me to discuss this further and I hope you will find me a suitable candidate for this job.
With best regards,
Richa V