Being Intubated is kinda like breathing thru a straw, it is somewhat difficult, but the airway is secure that way, plus air is being pushed to his lungs, vs. how we normally breath(our diaphragm drops and air fills our lungs like a vacuum). Most people intubated have some discomfort, so they usually give the pt medicine that keeps their anxiety low and also medicines like "Versed" this will prevent any memory of the event, so people are not traumatized by being intubated.
Breathing is not only a means of providing oxygen to the lungs. It is a way of maintaining the acid-base balance within the bloodstream.
"Breathing heavily" may be a function of the settings on the respirator, or it may be a means the patient is compensating for an excessively acidic blood.
There are unanswered questions, because the respiratory therapist has many options in maintaining the intubated patient. This is the person to have a discussion with. They are often difficult to speak with and shrug their shoulders when asked a question, referring you to the attending. But give it a shot.
One common problem is aspiration of water from the respirator. The therapists prefer moisturized air/oxygen and often the "bubbler" causes excess fluid to build up in the lungs. They are often resistant to change this protocol because of rigid hospital rules.
You have my sympathies and your father is in my prayers.