The way I seee it, haste gives you one partial action. A partial charge is a partial action. Then it is possible.
You answered the question in your final line: the restriction for a charge is with the action, not the round. Thus, you are not restricted to the straight line rule (because it is two different charges) and you don't need Ride-by attack. Your mount do need haste as well though.
You answered the question in your final line: the restriction for a charge is with the action, not the round. Thus, you are not restricted to the straight line rule (because it is two different charges) and you don't need Ride-by attack. Your mount do need haste as well though.