if it is 3 seats length-wise (rather than side by side), you should be able to get it in the monorail, no problem (well, ok, it might be a bit of a shuffle!!).
we take our triple Runabout (3 seats, front-to-back). we, too, just take the car to the parks when we have the stroller. my stroller WILL fit on the monorail, in any of the cars, but often the CMs will try and tell us to wait for the handicapped accessible car (which we then have to promise them that it WILL, indeed, fit in the other cars and we will not be holding up traffic!). the only time this bigger stroller is an issue (and keep in mind, our's does NOT fold down) is when the monorail is packed and there are already loads of people waiting at each door, in which case we wait for the next monorail to ensure that we have our own space.
our RA is also fine on the the ferry from TTC.
it can be a bit of a walk from the parking lots to the parks without the use of the trams, but with 3 young kids, you're going to want to get there at opening anyway

, so you can hopefully get a good parking spot! when we go back to the parks after naptime/rest time, the parking attendants will often let us check for parking spots up front (loads availableusually by 5 or 6pm!) when we explain that we can't get on the tram.
i can't help you with the airline, other than to tell you that plenty of triplet families have reported no problems taking their triplet strollers and having them checked-in at the gate. as PP mentioned, i'd call to double check and see about addtl. charges.
have fun!