Very few umbrella strollers recline and you really want to recline with a baby that age for naps.
I was going to say the same thing. A baby that small will really need to recline /nap. The baby's comfort will have a huge impact on the whole trip -- this isn't something to downplay.
I had a big stroller + a smaller folding stroller (never had an umbrella style). I really used both, but in those early months, I only used the big stroller. The smaller, lighter stroller was great starting about 1 year.
I'd just bring their everyday stroller. A) They'll know how to use it B) It already works for them
Well, since the baby isn't yet born, they don't know whether their waiting stroller works for them ... but presumably they'll have time to find out. Regardless, this logic is sound.
Another option is to
rent a stroller. We've been doing it for years. It is an extra expense.
Consider that you have two options for renting:
1) Rent just in the parks. If you go this route, you could carry the baby in a sling on the busses /pick up a stroller as you enter the parks. This also means you have to carry the baby's diaper bag on the bus, whereas if you have your own stroller, it'll ride along in the undercarriage bag. And it means that every time you enter /leave the parks, you'll have to wait in line to pick up /drop off. If you make this choice, definitely bring something unique to tie around the handle. Why? Because your stroller will look just like everyone else's.
2) Rent from a local place. They'll deliver a stroller (and other baby gear) to your resort or rental house. This would excuse you from bringing a stroller on an airplane OR using up a large part of your trunk space for a stroller.
My experience (with 15+ trips with a stroller) is that the baby's comfort and ease of pushing 100% outweighs the bus challenges that may/may not happen.
Sooooo true.