Received the wrong animated weapon

Previously i turned in my whm zeta and went through the steps to get the i200 relic weapon. I wanted also to do the same for my smn, but instead of receiving the smn animated weapon when i turn in my smn zeta weapon i recieved another animated seraph cane for my whm, which of course, I do not need. However the quest given to me for Snowcloak calls for the smn animated weapon. This i do not have so I am stuck as i traded in my smn zeta. I do not feel i should have go do the fates. I worked hard to get the zeta.

Im assuming its because you started the quest as a whm the second time too. Turning in your weapon gives you the crystals, which you can then use for any weapon, providing that you start the quest as the class you want the weapon for.

I had previously done the whm quests and had the 200 weapon which i am saving the unidentified items for. I wanted to trade my smn zeta in to get the quest for the dungeons and at least have the level 200 weapon for my smn. What i got was the Animated seraph cane for the whm to do the original dungeons but the quest call for the smn animated weapon. There was not choice given for the weapon. I lost my smn zeta and cannot proceed any further for the smn relic until this is corrected. I don't know of what I did wrong, if anything.

Sounds like you didn't start the quest again as SMN, and instead repeated it on WHM.

The choice is what job you are on when you start the quest. It tells you this in the active help text that appears when you first check out the quest.