Well after some research I reached the following conclusion:
With I was trying to do is not possible unless you set some limitations.
Only one of the two panels can render "actions" that are stored in the browsing history. If both panels render actions that are stored in the browsing history it's highly probable that navigation won't work as expected.
With this in mind I realized that what I actually need is to render the navigation aware actions in the left panel, and in the right panel render the other stuff(I call them utilities). For example one thing that I render in such a panel is a Chat-Panel.This is how facebook works with it's chat.
So basically I can user standard turbolinks to handle the requests which store browsing history and something like pjax for the "Utils" panel. The only problem is the Turbolinks completely renders the whole page, even if you send a small piece of html as a response.
To solve this I ended up using wiselinks, which is the perfect combination of turbolinks and pjax. Also, unlike pjax, wiselinks can even handle forms.