We travel with two Peg Perego strollers -- since DH is with us, I don't see any need to have strollers that connect, or to bring a double stroller. We zip around much more quickly when each only pushing one - and our strollers are easy to push, but still have all the benefits of a full size stroller (recline completely), yet they fold up just a little bit bigger than an umbrella stroller.
We also bring at least one carrier - at this point, the ergo is our favorite.
Bringing two strollers is nice b/c then when we only need one for the youngest, we leave the other in the hotel room.
I know you said you need one to push b/c of carry-on's, so maybe the connectors would be best (but I imagine they are even harder to push than umbrella strollers are on their own) - when necessary we put one kid in a stroller, one in a carrier, and used the other stroller for luggage. But really, our bags fit either on the back of the stroller, or were backpacks that could be worn. Also, our strollers both have a small step on the back so an older child can stand on the back - making it easy for one parent to push two kids at once (which is good for us, b/c we hapen to have four kids).Pic here
(just cause it's sweet) - 2 kids on the back, 2 in the strollers at Disney