They are showing what appears to be hospital surveillance video of the dad leaving the hospital with the child, which makes me wonder if he snuck out. If there was a court order then it would seem he was violating that order. (Here's a somewhat similar situation.)
exposes his very sick son to the intensity of his special pleading and some very absent-minded intrusive gestures ... his actions reflect someone who has lost all sense of reasonable proportion
Exactly. Obviously one objective was to show the child is ok, but he should have carried on his 2nd objective (developing support for his acts) without the child in earshot. He talks about how sick the kid is. Does the kid need to hear how grave his condition is? Then he talks about stuff no 5-year-old could possibly cope with--the police looking for his dad.
It was pretty horrible he kept the child in the room for that very adult discussion, but of course he learns no boundaries on that matter from his Mother org.