I believe the two cannot stack.
If you look at it like this, both pounce and ride-by-attack trigger on charge. But, Ride-By-Attack states that you can use an "move action and attack action" together as a standard action and then use another move action (which is effectively your full-round action. Standard+Move).
Pounce, as it also triggers on charge, allows you to move and then mount makes a full attack action instead of a normal attack as charge normally does (which is effectively a full-round action + a move). If you take out the common factor between the two, which is the move action granted by the charge action, you are left with a Standard attack from ride-by-attack and a full-round action (the full attack) from pounce. You cannot do a standard action and a full-round action in the same round, it's one or the other.
From that point of view, if I was the GM I'd rule against the two working together.
A simpler way to look at it is, pounce is move then full attack and once the full attack happens you can't move (as stated above by Ssalarn). The other way is ride-by-attack lets you move and attack and then move, but you can't trade a move action for a full attack action provided by pounce after the charge.
Hope that helps.