Do NOT count on them holding your connecting flight. Our original flight was late because of a problem of Delta's flight and our 60+ minute connection in Detroit was cut to 10 minutes and we had to change terminals. I sent DW ahead to talk to the gate agent, but they wouldn't hold the flight. Then, when we got to the connecting gate, they were pushing for our passports (international flight), which was in our carry on and were a little rude while I was getting them out.
OP, normally I'd say there's no problem with an 80 minute connection, and there probably isn't for you, but the car seat does have me a little concerned (depending on the size of it). I agree with trying to get toward the front of the first flight if possible. Alternatively, look on Delta's website and see if there's another connecting flight (or earlier original flight) you'd be willing to take. Don't worry about the prices. Call Delta and explain the situation and see if they'll change your flight for free. Tell them you're concerned about making the connection with two young kids and a car seat. The worst they can say is "no".