Perhaps the trickiest portion of your trip will be actually boarding the plane and getting settled in your seats. Juggling carry-ons, equipment, and babies in confined quarters is never easy. But there are some ways to make it go smoothly.
Take advantage of the pre-board option. Most airlines provide an opportunity for families with small children to board the plane ahead of time. If you do not have assigned seating, this is your chance to pick out convenient seating. There is no rule that says your entire party has to board early. Let one parent go on early, carrying the bags (and car seats if necessary) and getting the seats set up, while the other remains at the gate with the children.
If you are able to gate check your stroller, keep your twins seated in it as you enter the jetway. You can't roll them straight onto the plane, but you should be able to go right up to the door, then leave your stroller to be checked. It should be waiting for you when you land. Again, if you can, have one parent stay seated with the children while the other gets the stroller ready and manages the bags.

