For anyone who finds themselves with the same problem, we figured it out.
After removing and reinstalling the new clutch a second time we had the same results. The release bearing would not snap into the pressure plate. I went to the local parts house with my VIN number and had them check the part to make sure we had the correct clutch kit; which we did. They had another kit in stock, so I bought it, installed it the same way as before and it worked as it should have. The release bearing snapped into place and the pull clutch works great. I returned the defective clutch kit to the parts house for a refund. No more problems.