i know that there is good and inexpensive guided fishing to the north of cancun and they'll pick you up at the resort. i think that the diy could be a bit dicey. you best check out the safety issues when wandering off on your own beyond the resort areas. don't forget, it's mexico, not disneyland.
rods and reels on the plane have traditionally not been a problem, but i just came back from an overseas non fishing trip and i can tell you, the security is much tighter and much more arbitrary-at least in the u.s. the tsa people are all running around like chickens with their heads cut off-seeming to make it up as they go along. it would be comical if it wasn't so pathetic. anyway, here's no telling how they might deal with rods and reels in the current environment.
flies have always been a hit or miss affair-and large flies more of a problem. i always pack them in my checked luggage.
for whatever it's worth, i do a lot of fly fishing travel and have always carried my rods and reels. i'm going on a trip to the amazon this thursday and will be checking all of it. i don't want to risk that they refuse it at the gate or in the security area and it doesn't make it to the plane.
good luck and have a great vacation