If you really haven't flown with kids, it isn't terrible. Gate check your car seat, nothing will happen to it. Most parents overthink how much their kid will piss other passengers off, when in reality it doesn't bug a lot of people. Most people just pop in their headphones or AirPods or whatever, and can't hear it.
Have a change of clothes ready for everyone, probably two for the kids, plus plenty of diapers in your carry-on/personal item. Bring plenty of snacks. We travel with our kids (both under 6) multiple times a year and use one of their personal items as a backpack full of clothes, snacks, diapers, formula, whatever.
The only time I've ever had an issue with another passenger on a flight with my kids is when some boomer asked if our baby could stop staring and her and if he could face forward.