As a former Flight Attendant, I agree with the others. Check the suitcase. I'll plead another case. When people see you carting that darned thing, they'll wonder why you are, especially with twins. Also, wheeled suitcases are not very popular with Flight Attendants. You'll get more sympathy, and perhaps more help, from the crew if you are NOT dragging unnecessary items on board.
If your airline charges for bags, consider this an expense you'll have to cough up until your children are a bit older. Keep it in perspective that you're flying alone with twins so make life as easy as you can.
Take these ideas people have given you and try them at home first. Put it all together and wheel around the living room, garage or even front sidewalk. Just get an idea of how it will work before the travel day. Remember bungee cords are your friends!
I actually recommend that you come up with more than one way of carrying it all. You might want to purchase something which you can wear one car seat on your back.
Loose your purse. Either put it in your checked bag or take what's necessary and put it in the backpack you'll use as a diaper bag (or backpack-style diaper bag). I then take a very small purse on a string around my neck, or a "bum bag" will work, with the essentials like my cell phone, wallet, etc. A really small one wont even be noticed and it's an exempt "personal item".
Check the suitcase but be careful of any baggage limits. So many times people try to stuff everything in one bag and then get nailed for it being too heavy at check-in. Weigh it and make sure you don't need another checked bag. You have three seats and each baby has the full allowance.
Go on line and order any baby and your personal products you need, diapers, shampoo etc. and have it delivered so you don't have to drag anything more along than necessary. Be sure the bag is mostly filled with clothes. Or, if you have a nice mother like I do, "order" from a relative and let them shop for these things. Anything left over can be used on a future trip or by your hosts (maybe not the baby food jars
One small point; please don't put any luggage carts in the overhead bins. This was not allowed by either of my airlines, especially after one passenger was seriously injured. You know it's there and you'll be careful but the impatient person two rows back wont when he grabs his bag in a hurry and it flies out. Throw your luggage cart on the floor, under the seat in front of you. The last thing you need on this flight is any drama from another passenger!
Try to fly early in the day, when children are in better moods and flights are more likely to be on time.
On-line check-in is great when you're flying with kids. Southwest (WN) does pre-board but only between the A and B groups. Check-in on line within 24 hours (do it
exactly 24 hours before) and you'll be in the "A" group. Even if you're not flying WN, find out if your airline does similar. On-line check-in also saves time at the airport.
You might get questioned by the crew on board, used to seeing lap babies. Tell them that you have purchased two seats for them to avoid confusion. Sometimes too, they check if there are standby's trying to get on. Sorry!
My guess is that you do get some help. Remember that once you get past security, that is a closed area with only passengers and employees. No guarantee but it's not a public area like where you check-in. After security especially, if someone offers, take them up on it. Think ahead of time, if someone asks, what will you ask them to do? Thanks, here's my diaper bag! Mind dragging this contraption with the car seats? It's not really that heavy... I didn't allow people to take my children but I did take them up on things like watching them while I collected my checked bags. They've even collected my suitcases off the belt for me (and if you saw what I drag across the Atlantic, that's
very generous!)
I'm now the one offering. Since my kids are older, they'll play with smaller children and I'll offer to carry something or drag my son into "service". I think it's easier to say yes to a fellow mom with kids.
My flying tips are in my siggie. Good luck finding a good way to organize your things (without that pesky suitcase!)
I think you're very brave to attempt this. Even thought it's a short flight, it's not really that different. Thanks goodness you don't have to connect or go through customs! I think you'll be glad you did it and it wont be as bad as you think.