Integration with two rails applications

Ive build a academic application where users can open tickets, something
like a help desk.

I want this tickets to be opened in Redmine, when the tickets get
updated on Redmine, update on my software too, when the user update on
my software, update in redmine.

I thinking in how to do this in a smart way, what you guys think?

plugin to Redmine?
database integration?
forget Redmine and do your own ticket system?