There’s no need to shlep your outerwear onto the flight. Once you get into the airport, keep just a light sweater and stuff the rest into the check-in luggage.
Keep your stroller until the last possible moment. Because you have to leave your cart at the security check-in, you can use your carriage to carry all the bags. If your flight is delayed, your baby has a comfy place to nap. Typically you can keep your stroller until boarding and then check it just before you step on the plane. Each child can have a stroller and a car-seat and you can usually check in a pack’n’play as well.
Limit your carry-on to as few bags as possible. It was such a headache getting our total of five carry-on bags, along with our coats on board. My husband actually had to make two trips, even with the help of a wonderful flight attendant. Find out if your flight offers pre-boarding for families. Ours did, and we opted to do that because I was worried there wouldn’t be enough room to store all the carry-on bags near us. Then there are times when boarding at the last minute to give the children the maximum amount of time to run around and burn excess energy makes more sense, so that is something for you to decide.