Take the double stroller. It will count as ONE carry-on for one of the kids, instead of taking 2 strollers and having them each be the kids' free carry-on. As for security, I just took my daughter to Scotland and one airport put the stroller through the x-ray machine, while the other wanded the stroller w/my daughter in it. I offered to take her out, but they said it was ok w/her in it.
When you get to the gate, if you need help, let the gate agent know. Get on the plane before everyone else, because when you get to the end of the jetway to get on the plane, you have to check the stroller and they will put it under the plane, and they will have it waiting for you when you get off the plane. You have to put a tag on it, so get the tag when you first arrive at the gate. If you're like me, you'll have diaper bags, carry-on luggage, etc. in the stroller that you'll have to take out and get on the plane w/the kids, so this is another reason you'll want to get on the plane first, so you're not holding up the line of passengers behind you. If you're still not convinced, contact your airline and ask them if there are any restrictions on the kind of stroller you can bring. Know that w/many airlines, if you are on a domestic flight, you only get either a stroller or a car seat as the child's free carry-on now, and they will charge you for the other item if you have both with you. Best wishes on your travels. I wish my hubby could have gone w/me...would have been so much easier! ~C.