As a first timer, I highly suggest bringing a stroller.
You know your kids best, but I found great comfort in knowing that in huge crowds that DD was strapped and not getting lost in the shuffle. She is on the small side and I know there is no way she could keep up with her brothers. Also my DD8 is extremely small for her age and her leg simply cannot keep up. So one stroller was shared.
We loved having it at the resorts and especially DTD where the crowds get huge and the stores and very easy to lose sight of a child.
I hope your DH comes around to the stroller idea. After reading many post here, the Maclaren one was a lifesaver. Carries up to 55lbs, folds super easy and has a carrying strap. It is an umbrella stroller that beats any light weight stroller I have every used. We purchased especially for the trip. It was the best $100 I spent. There were some nights when DD8 sat in it and DD5 sat in her lap. It was a breeze puch even with both of them init. Renting a stroller can add up $$ and we really wanted to have one at the resort, etc.
I think if you find that you do not need the stroller you can leave it in the room, but if you do need it you'll have it.
Having at the airport was awesome, again we knew where DD was, safely buckled in. It was for DD and much as it was for me. I hope your DH reconsiders. But again every child is different.