I had the experience before. 2 year old and 6 year old. No big deal.
I bring a stroller, 2 carry-on backpacks. One for me, one for my 6 year old. That is it.I didn't bring a car-seat with me.
I can put the backback into the lower level of my stroller while in the airport.
Make sure your kids follow you strictly. Your bigger one should help you a lot. Educate them before your departure.
Good luck.