If I were to set myself up to brace for a charge with a Longspear, do I get both my readied attack for double damage when they move into reach and my attack of opportunity for normal damage (or would it be double still because they're still charging?) for when they move through my threatened area, assuming they don't also have a reach weapon?
The actions happen in order, first the enemy enters a square that you threaten, triggering your readied action (assuming that you specified the 'charges me' (and thus enters my threatened area) as the trigger) for double damage (as this attack uses the spear's special property).
SRD text for a spear (emphasis mine):
If you use a ready action to set a spear against a charge, you deal double damage on a successful hit against a charging character.
The next thing your opponent does is attempt to leave your threatened area, triggering an attack of opportunity as per the rules of AoO. However, this attack will deal regular damage as this attack is not performed because of a readied action.
Specifying the 'use a ready action' in the spear's property line implies that it only applies to the attack that is triggered by that ready action.