I believe I may have a bad hose leading to the resevoir that holds the antifreeze or maybe the resevoir itself is cracked?

It could be the hose. Unless your car has ever been hit on that side, the reservoir usually outlasts the hoses.
You can easily test the hose. Unclamp it from the reservoir bottle when the coolant is not hot, plug the end with your finger and hold the hose down lower than the other end that is attached to the radiator fill neck. Look for leaks.

To check for cracks in the reservoir, it's easiest to place a flashlight inside the bottle top and look at the outside of the bottle...if liquid can get out then light can too.