i find bringing as little as possible is the best way to travel. bringing too much may compromise your ability to keep the kids safe and entertained. if not entertained, even good ones may get restless, do something out of boredom, or who knows. every rental car agency has car seats to rent and I believe there is a site that rents things to parents for babies/kids like strollers, seats, etc. I fly a lot too but never alone. My child loves and we will be going on a 9 hour flight soon, one way! So what I recommend is to bring a bag of toys, new and some of their favorites that can be stuffed under the plane seat. Hopefully, someone will meet you at the airport once you get there but if not I am sure you will be fine. Remember the children take their cues from you so think and act fun adventure! I try to let my kids be involved as much as possible even in the packing. Keep in min that my daughter packs the most outrageous toys but even when I pack her favorites she hardly plays with them. Think snacks (maybe even a treat that makes it "special"), a portable dvd is a wonder (you can get lots of suitable movies on Ebay or buy used at half.com!), and some players even come with two earphone jacks!-- although my kid never puts them on! I once flew with her when she was 16 months and I remember she was more fascinated with the plastic cup the steward gave her than anything else! What I am trying to say is, you can plan but believe me the best thing to do is relax, have a good time, and think about how & what will entertain! Also bring a light sweater, my daughter is always cold!
Problems you will encounter are at the security check in where the portable devices, cell phones, shoes, and so forth must be checked separately which means unpacking it and repacking it so think about placement when you go to pack. it helps to be organized. also, the no liquid rule is a pain but you can buy milk, juic, and so forth on the other side of security. many airlines will let parents with small kids board early. i never do this as it gives them more walking around time, running in a circle. if you can walk as much as possible before boarding to tire them out a bit! another problem will be the potty, both on the airline and off where you will drag everything around. i hope all this helps!