Why would your legs shake badly after exercise?

You say you are working out hard! Are you cooling down gradually or are you stopping your exercise abruptly? If you stop abruptly your circulation will be challenged and lack of oxygen to the muscles will cause them to spasm.
Get advice from a trainer about all aspects of excercise eg fluid intake, warming up and cooling down periods, working aerobicly and checking your heartbeat etc etc etc.
Exercise without proper understanding of your body's needs is PUNISHMENT!