If I wear Hide armor (Check -1) and use a Heavy Shield (Check -2) is my check -2 or -3?
In other words, do the checks stack or do I use the highest negative?
They do stack. You won't find any help in the rules for Armor or Shields, but the Rules Compendium (p 314) has a general entry for penalties:
Shields and Armor are different game elements, so the penalties stack.
The short answer is the penalties stack.
Source: page 275 of Player's Handbook states:
On this page, it also separates out armor bonuses and shield bonuses (or conversely penalties).