If you plan to use the default bottombar as navigation, you are going to have a hard time. If you have your own button-based navigation it's quite easy to do with a data-source nanoflow and some styling.
I have created a custom navigation bar as you suggested.
Now for doing navigation, I am using show page activity on click action which is adding a page with the different transition effect than the inbuilt navigation. Is there a way that we can use the inbuilt navigation of Mendix so that the transition of page will not affect the user experience?