At those ages the double stroller is the way to go. You strap everyone in and then can take a breath to get everything done you need to do to get to your flight.
It will be a bit tougher getting through security if they make you put the stroller through the xray machine.
I liked the previous poster's idea of 2 umbrellas...or you could umbrella the baby and then get a backpack with a leash thingy for the 2.5 yo...depending on how you feel about those types of products. (I always figured if I loved my dog enough to put her on a leash so she didn't get hurt...how much more do I love my children).
If your husband can keep hold of a 2.5 yo's hand the whole time...good luck...he lets go once and the child runs or even steps away...you can't see them in a crowd, they are too short...
Remember everyone has to take off shoes, including the children...so the worst part will be getting through security with either stroller, take on bags, and no shoes. Good luck and safe trip.