Here’s a developer’s description of the Nature’s Grasp change. It does appear that you will be able to have more then one roots up at once.
Nature’s Grasp is a self buff that causes things that hit you to become rooted. That effect now has 3 charges. There is a small internal cooldown in between roots to keep say a rogue who hits you twice very quickly from wasting two charges. In your example, both the DK and pet should get rooted. If the DK breaks the roots and gets on you again, they will get rooted again (subject to the 45 sec duration).
The intent of this spell was to be a defensive tool for druids. Since it hasn’t quite kept up, we wanted to try to get it to be more useful (i.e. do its job) rather than come up with an entirely new mechanic.