Had a Gardener heir survived the Field of Fire, how would that have reshaped the power dynamics in ASOIAF?

This is an interesting question, because huge chunks of Westerosi history change as a result, as discussed here and here. In terms of power dynamics, the Gardeners would be far more secure in their rule over the Reach than the Tyrells have been, as like the Starks and Lannisters, they have been kings for all of recorded history, and even more so than either of those, they have the whole succession of Garth Greenhand to reinforce loyalty from almost all the major houses of the Reach.

So as I’ve said before, you’re going to see a far more unified Reach when it comes to national politics, so if it gets involved in civil wars and rebellions, it’s not going to split. Which is going to make the Reach have much more weight in those conflicts, because whoever they side with is getting 100,000 men, a huge fleet, and a LOT of the food in Westeros. 

Moreover, the Gardeners are not going to have the same status anxieties as the Tyrells, and thus will be less eager for royal favor – which means they might be less willing to contribute so many tens of thousands of men for ruinous invasions of Dorne, or to fight for the Mad King Aerys. Indeed, given how Mern IX acted during the Conquest, it could well be that once the dragons die out, the Gardeners might start challenging the Targaryens in an attempt to regain their independence.