When I type in the Item Name (internal name like your TA50) on the 2nd vendor, I get an error that says Duplicate Entry.
I still do not know how to do this.

This is the most SIMPLE thing that should be basic programming.
How can QB assume that a raw material that goes into an assembly will have the exact same PN for several different vendors???? If I make a separate ITEM for each of the vendors, exactly HOW will I make an assembly? 

Item REDSCREW (inventoried part) is sourced from 2 different vendors. Vendor 1 calls it REDSCREW000, Vendor 2 calls it REDSCREW999. Item REDSCREW goes into assembly REDTOY. I need to be able to buy the red screws from whomever has them in stock the cheapest. When they arrive into inventory, I need them to be used to make the redtoy. I don't care who sent them.
You are telling me I have to make 2 SEPARATE inventory items for this same screw???? Then how do I make the assembly? I can't call out both screws in the assembled item! 
There is no place in the assembly item where I can call out Alternate items in case one is out of stock....so that won't work.