I feel like I've been fortunate with my 2 kids so far, but one's still in the easy stage (4 months) and we've only done one road trip and one flight with him.
I think this somewhat reiterates what others have covered but here are some of my general tips for travel with young kids by plane:
1) Avoid nap times and after bedtime for flights unless you know your kid will fall asleep in a carseat and they will be in one (not always true in that lap infant stage!)
2) Airlines will often give you an extra seat for free if there's extra space on the plane and you have a lap infant. Call ahead or indicate lap infant at booking and some airlines will do what they call an "infant block" - a soft block that can be sold if everything else is.
3) It's a toss up on whether to take the car seat to the gate or not. If a lap infant - I wouldn't bother unless you're really hoping or already have confirmation of that extra seat. With an older child... well, the car seat moves them forward, so there's a chance you're actually make it even easier for them to kick the seat in front of them.
4) SNACKS and REST are amazing. Do your best to have them in a good mood arriving, and have some things to entertain them.
For travel by car, I can speak from the experience of cramming 3 adults and 2 littles into a Prius for a trip where we stayed in 3 different hotels...
1) Staying in one place for multiple nights reduces your stress a lot. Packing and unpacking when you've got diaper stuff, toys, bed/travel crib stuff... is a pain.
2) Keep snacks, drinks, and toys accessible in the car. I got so annoyed at the other adults who kept moving stuff where I couldn't reach it. I was the one crammed into the back with the two car seats and I couldn't always get to things that would've made my life entertaining them much easier.
3) It's possible even with 3 adults and two under 3 to share a single hotel room with 2 beds. I shared a bed with my husband, the other adult was in the other one, we had a travel bassinet for the baby (amazing and folds up really small!), and for my too-big-for-pack-n-play almost 3 year old, we just brought the bottom part of the pack-n-play to put a familiar sheet around and then had him sleep on the floor.
4) Prepare for falling asleep taking a LOT LONGER. Even if your little one(s) are in their own room, but especially if you'll all share one room or if they're in a stage where you can't confine them to a crib or bassinet. You're likely to have some skipped naps unless you have a good car napper, and they're in a new place where everything is interesting and there are new ways to get in trouble. We tried to contain our almost-3-year-old by doing things like turning a table on its side and containing him with furniture, but it's still difficult. And I'll also mention that it gets easier every night that you stay put.
5) Acknowledge going in that it's not going to be perfect. There will be crying. There will be potty accidents if you have recently-trained kiddos. Whether or not your kid is on the Autism spectrum, has Aspergers, or is not any kind of special needs, traveling with kids throws them off and you will have an amazing time during the good moments and pull your hair out during the bad.
AirBNB and VRBO in a single location instead of the different-hotel-every-night approach will be what I'll try for in the future. We cloth diaper so doing laundry if it's more than 2 days somewhere is essential and staying in homes makes that nice and easy, plus you can sometimes put the kid in their own room. My older son once slept in his pack n play in a large bathroom/laundry room, and I've definitely put him in closets, too!
So for me, in the end, the biggest tip is to just GET WHERE YOU'RE GOING and stay put for a little bit so that you can actually enjoy it. Then make short day trips from there. I just chalk up travel days as lost time where hopefully no one goes insane.