[Hula Doola]

Not certain I have understood your travel plans properly, but as I believe if you are booking connecting flights and the first is delayed preventing you catching the second, if you booked as a package with the same airline they are responsible for providing you with the next available flight. But if you book separately and miss the second flight for any reason they do not have to help you with this and you may have to pay for an alternative flight.
If you are breaking your journey with over night stays then it might not be any benefit, and you'd be unlucky to be that delayed!