Hi, I know this is a bit old, but have you had any luck with any of the yarns? Some of them rang distant bells, LOL and in looking at Hobby Lobby I believe some of them could be from there.
The link is to my search for 'rainbow' under yarns. In case it doesn't go to the page cleanly, I went under yarns by brand, and then down the left I searched for 'rainbow' in the color area. The rainbow in your pictures reminds me of HL I Love This Yarn; the twist and the skein shape are similar. It could also be Joann's but the color schemes don't say Joann's as much as Hobby Lobby. The same is true of the other yarns for me.
I know there is a way to use google to search by using your picture. I've not done it, but you could give it a try. It might pull up an old image with a name.