given that you have only 13 days, i would avoid train journeys unless they are less than 5 hours long....
there is not much to do in mumbai & i would cut it out of the itinerary if i were you....if you can fly in & out of delhi instead then you would be saving yourself a lot of time....
if you can't change your flights then just use mumbai for transit....all the other places have much more to offer....