Hi! And welcome!
Traveling with multiple strollers is doable, but definitely tricky, especially when your hands are so full! I have a 5 year old and now 10 month old twins. We went when the twins were 5 months old and we've gone many times with just my daughter.
I would recommend using a baby carrier for the 7 month old and using a backpack as a diaper bag/park bag to keep your hands as free as possible.
The larger double strollers-- such as a jogger or the front-back graco double will fit on a bus. Many of the buses are lower to the ground (one step up) and have wide aisles. My husband usually carries the strollers and he goes directly to the back door and stands there holding the strollers. If the bus is empty, then there's absolutely no problem and he'll take a seat. Sometimes you can ask the driver if he'll open the back door for you to enter with the strollers instead of using the front door-- seems to depend on the driver and the time. We also jam the strollers in between the seat sections-- there's a bit of a gap between the groups of 3 or 4 seats.
When the buses are full, we usually wait for the next bus. We want to make sure there are seats for the kids and room for the strollers, so we don't mind waiting.
We take a double and single Combi stroller. Both have straps, so they're easier to carry and very light weight. We now have a single MacLaren Volo to use in place of the single Combi, but it also has a strap.
If you drive in to any of the parks and need to take a tram from the parking lot, be sure to use the last row in each car. They're a bit wider. You have to fold up your stroller for the trams too.
If you're staying at a resort that utilizes boats, you usually don't have to fold up the stroller.
Good luck!