Speaking as a mom who made several 2 stroller trips. then several more 1 stroller trips and finally graduated to no stroller trips...can I PLEASE beg you to NOT take 2 kids, 2 adults and 2 strollers that are bigger than my first car and fully loaded with paraphanalia!!
We made our first trip with the mega stroller and 1 umbrella, and it took me until about the 3rd day to decide that it was a mistake. Thereafter we always took 2 basic umbrellas.
The kids spend only short periods of time in the stroller without getting out for rides, etc. They can hop in and out faster, the umbrellas are MUCH easier to navigate in crowds (only a problem for all those people you plow into in those huge vehicles) and some bit cooler in hot weather.
For under $20 at
Walmart you can get an umbrella stroller with a shade canopy and a decent sized basket under the seat. they weigh about 3 pounds, can be folded with 1 hand and easily carried over 1 arm while carrying a sleeping toddler...if money is a huge concern you could take it to a consignment store when you get home and sell it for $10 or 12...but by your second bus trip you will be patting yourself on the back for being so clever and getting them.
It will only take 1 bus ride on a crowded bus when you and hubby are hanging on to 2 huge strollers and 2 kids and trying to remain upright before you would feel the umbrellas were worth the investment!!
Our last trip I was behind a couple trying to get 2 gigantic strollers folded (of course they didn't start unloading the 14 bags and 6 sippee cups until they were in the door of the bus), then there were not nearly enough hands to hold kids, and stuff, much less the strollers, so Dad makes 3 trips onto the bus to drag it all on (while 40 other hot tired people wait) by the time they are loaded the entire line is either highly amused or totally annoyed.
The lady behind me had 2 toddlers in 2 umbrella strollers, they hop out, she kicks the strollers shut, hangs both of them over one arm, grabs one child, hands the other to Grandma and they hop on as fast as everyone else. We are chuckling at the family still trying to rearrange and the woman with the umbrella tells me she ran to Walmart in Orlando after their first day at the parks because she said "she could not take another day lugging the Graco"