If I'm reading this correctly, you have the following problems:
1. When you use your Hornady die, the projectiles can be moved by hand (spun, moved up or down in the case) - basically there is no neck tension on the projectile.
2. When you used the bought brass without sizing, there was adequate neck tension?
1. Mic the expander ball on your Hornady die and make sure it is within spec. It almost sounds like the ball is oversized.
2. Take one of your sized cases from your Hornady die and mic the outside diameter of the neck after you run it through the die. Then mic the inside diameter of the case mouth. If one or both of those is out of spec, you probably have a die that Hornady needs to replace.
3. Just as a general rule, I would NEVER rely on brass that has been "resized" before I procured it to be actually resized. Never. Not once. You are taking a gamble with that.