What you are trying to do is totally doable.
- Create a new project: Single View Application
- Open Storyboard and select the ViewController
- Editor / Embeded In / navigation Controller
- Add two UIButtons to your project
- Add 2 TabBarControllers to ypur project
- Connect every TabBarController to one UIBUtton through Segue Push
- Ready. Your idea was drawn.
The result in this image.
An example project here.