Pounce would allow me to make a full attack on the end of a charge. This bonus also applies on a mounted charge. However, what happens if I combine a mounted charge with a ride-by attack? Can I still make a full attack against my target, or not, since the square he occupies is not (strictly speaking) the end of my charge.
Despite the awkwardness of the situation, yes, you can.
Ride-By Attack itself details how it should be handled. It's mechanic is separated into two steps: normal charge and additional movement.
"Normal charge" part works, well, like normal charge. So, if you are allowed to execute full attack at the end of normal Charge action, you can execute it at the end of the first part and then go to the second one.
As I mentioned above pounce on iteratives sounds awkward for me. Still, awkward or not, rules do allow that, so untill your DM bans it, the combination you want may be executed.
When your mount charges, your own pounce isn't applicable
For reference, this answer is based on the Pounce special ability's wording in the 3.5 SRD:
When a creature with this special attack makes a charge, it can follow with a full attack — including rake attacks if the creature also has the rake ability.
The basic rules for mounted combat use the following wording:
[...] Your mount acts on your initiative count as you direct it. You move at its speed, but the mount uses its action to move.
If your mount charges, you also take the AC penalty associated with a charge. If you make an attack at the end of the charge, you receive the bonus gained from the charge.
You direct your mount to make a charge, which is not the same as charging yourself. This means that a human riding, say, a tiger, can direct it to charge and pounce (using the somewhat misnamed 'fight with warhorse' Ride option). But a catfolk riding a horse can't use his own pounce ability with his horse's charge.
To me, this seems to also make more sense from a thematic/narrative perspective - a tiger or a catfolk can pounce thanks to their own agility, covering the distance to the target in one swift leap. This isn't the case when they are mounted.
Finally, the rules for mounted combat also have this to say:
If your mount moves more than 5 feet, you can only make a single melee attack. Essentially, you have to wait until the mount gets to your enemy before attacking, so you can’t make a full attack.
Which also seem to indicate that pounce shouldn't apply.
Personally, I'd allow pounce-while-mounted for situations where both the mount and the rider can pounce, e.g. a catfolk riding a tiger (it's just too thematically cool to disallow), but we'd treat that as a houserule...