There is no clean way of doing an internal redirect to another application module like that. I would think that if these two runmodes are related enough to share the same parameters, then perhaps they should be in the same modules.
If you do not want to put them in the same module, you may be able to solve the problem with inheritance. Make module Foo inherit from module Bar, and then Foo will automatically have access to both runmode 'mode2' and 'mode1', so you can do a simple internal redirect from mode1 to mode2 using 'return $self->mode2()'.