ATOBTTR

I've found DL to be very good about schedule changes most of the time when it involves a shortening of a connection (though DL rarely will rebook you from a connection to a nonstop as a favor, at least IME). But I do understand OP's concern about the time. 1 hr 20 min sounds like enough time and it is for most of us and OP would likely make the connection (which is why I said "it should be fine" above), but even 1:20 leaves little time do much else when small kids and car seats and such are involved. Could easily take 10-20 minutes to get off the plane, and another 10-20 minutes to get from one gate to the next. At up to 40 minutes to do those things, that means OP is getting to the gate as the pre-boards (which OP would be) would be boarding for the next leg. Doesn't leave a lot of time to go get food, go to the bathroom, etc. which are all things that take even longer with kids, which if OP has to stop to do, would mean getting there and boarding with the masses, which would be far more of a headache for OP and others. While DL didn't have to do anything per the CoC and its policies, DL saw it as the right thing to do to make OP's life a little easier.