As Pyrodante says, Loki has an inferiority complex - he's never been able to live up to his father's expectations (by his own measure), he lives overshadowed by Thor, and he's generally considered weak.
He doesn't just want power, Loki wants everyone to KNOW that he has power. Loki isn't mad, insane, or anything of the sort - Loki is a mastermind. His flaw is his crippling inferiority complex colored by his desire to do things in roundabout ways (which is also a way of overcompensating for his inferiority complex, he wants people to respect his genius).
Loki is arrogant, power-hungry, and defiant. Sneaking frost giants in through the hidden ways wouldn't appeal to his needs. Once he has made his power grab, everyone is supposed to know. Tormenting Heimdall is part of that - He wanted to show Heimdall that he, Loki, was in charge now.