I got about 15 rooted peices off of a neighbors tree and put them in potting soil. The first few days they kinda looked up and down but now seem to be staying pretty perky . I trimmed down a lot of the leaves at first so it can focus on recovery. And have been keeping them in the shade.

My question is...I have a greenhouse that is fairly warm but vented. Is it beneficial to move them into the sunny greenhouse or should I keep them in the shade longer.

I would keep them in the shade until they recover and start producing new buds. You could give them some diluted super thrive which would help the plant produce roots/ reduce transplant shock. But if you have 15 separate suckers and are curious you could always just move one to the green house and see how it does. 

Ditto !