So I have clear 2 of the 3 dungeons and retrieved 2 of the amulet pieces. However The third dungeon (the one near Winterhold) says it requires a key to open? I only received 1 key from the dungeon near Ivangaard. But it doesn't unlock the dungeon.

What do I do? Am I missing some random key from somewhere?

You aren't missing a key that dungeon is tied into another quest and Bethesda doesn't know how to prioritize their quests so that you can't get Forbidden Legends until you get that other quest, the quests use separate dungeons, or the dungeon insides reset and door locks when you get the second quest. I think Mage College takes you there but I'm not sure, check one of the 2 wikis.

I had the same problem.

You only get the key if you become a Mage.

Talk to the person in the entrance of the College that you want to become a Mage.

I was very upset about this because I was playing a thief and I had to become a member of the mage's guild to complete the quest.

Yeah, the first quest for the Mage's Guild takes you inside of the 3rd dungeon. The reason for this is that the NPC that goes with you inside of Saar is needed for the boss kill. It's a very quick trip to the mage tower then you're off to get the 3rd piece of the amulet.

Thank you for the fast responses!! I'll give it a shot and see what I can come up with

Thanks Again

There's honestly no reason NOT to do the mage guild questline - sure, you wind up with an honorific you don't maybe want (unless you're a mage toon....) but the rest of it's pretty nice - free house mostly....