Delta gave my SIL a large plastic bag for my 2.5yo niece's carseat to be gate checked. So even if you don't have a carseat bag, they'll have something for you to put the seat in if you ask.
I would, however, definitely recommend putting them in the carseats on the plane. Maybe not the 3yo if he'll stay in a seat, but definitely for the infant. We flew from Myrtle Beach to Charlotte on July 4th with my then 4 month old daughter and we had a very, very turbulent landing in Charlotte due to bad weather. The plane was literally jumping and dropping hundreds of feet at a time and turning side to side so much that all you could see was sky out of half the plane and land out of the other, and we were not making a turn! It was so bad that the pilot had to abort the landing and fly back to Columbia, SC to wait out the storm. I really thought we were going to crash, and was so relieved, like the rest of the plane, when the pilot started going back up. Luckily we had a seat for my daughter and she was safely strapped into her carseat and slept through everything. I know if I had been holding her I would have been terrified because as tight as I think I can hold her, when the plane suddenly drops, you're not prepared to hold them as tight as necessary and they could easily get hurt. I'm not even talking about flying out of your arms, though I know it's a possibility, but simply hitting their head on an armrest, tray table, etc. My daughter is also breastfed and nursed on every flight she's been on (which is 8 now), but I also bring a bottle of pumped milk so that she can suck during the landing and not have ear pain.
So aside from the safety during the flight, you also don't have to worry about renting seats at your destination, the condition of their seats, and also you'll have seats you and your kids are familiar with.