Well, in the Comics you very RARELY saw anything of Frigga, and Loki was there side by Side with Thor going through all the "trials" to become worthy of Mjolnir.
Loki had EVERY chance to do those same trials but didn't and was ALWAYS focused on how much more attention Thor got from Odin than HE did. Basically if Loki did the same trials and passed them where Thor might not have, ownership of Mjolnir might be different
Edit: in the 60's Loki was more or less always trying to steels the Asgardian Throne.