Here are a few tips that we learned traveling with little ones.
First lets talk about the stroller, for DH and I no way would we have done the umbrella stroller at this age, for a couple of reasons, using the larger stroller gave them some where to laydown if needed, delayed planes, long lines through security, secondly it was familiar to them, and lastly we could use the underneath storage area for their stuff which helped with carry on's and their day bags, also if you end up carrying them the kid's, you have a bigger spot to put your stuff. Also you will want their regular stroller in the parks so just bite the bullet on this issue.
Try to get TSA pre checked this will help with the lines.
Once you get airside, look for an empty area that the kid's can get out of the stroller and run around in this case toddle around, We would get airside and DH would find a empty area that the kids would get out and burn off some energy before boarding the plane, including walking all over with them we would take turns walking around with them. Also with more adults than kiddos' you can do what we did a few times, My mom and I would board with the stroller, and carry on's and the kids back packs, then DH and my Dad would wait to board almost at the last minute to give the girls every chance to burn off the energy before having to sit for 2 hours. Mom and I would be ready with the supplies for the kids, so when the came down the aisle they hand them in, sit down and everything was go to go.
Make sure to change them right before you board, trying to change a baby on a plane is really hard. I have had to do it but I took a tip from a friend and used pull ups so I did not have to lay them down to change them, it was awkward but I did manage it, and it was so much easier getting the pull up off and on then fighting with a diaper. make sure to have a diaper bag to tie up the dirty diaper the other passenger will appreciate it... Limit the apple juice or anything that seems to make them go poopie right away.
Bring on the I pad's, with games and movies, now is not the time to be worrying about screen time... its about getting from point A to point B without a full on meltdown.
Bring a variety of their favorite snacks. Buy bottled water and juice airside for everyone, it was a life saver when we got stuck out on the runway for 20 minutes.
Bring new toys that they have never played with, just small items should keep them busy and only give them to them on the plane.
There is always a discussion about med's and giving them to children when flying. This is something that maybe your DD should discuss with the kids doctor. Also if they are noise sensitive maybe some head phones... if you go with them let them use them before you go, so they are familiar with them, they also work great during the fireworks.