I've seen some of these and other images like this before. And I know that the grandchildren is fond of him, but I've seen him with them in documentaries and I found him very controling.
He can be, but I don't thank that's a bad thing. With normal as well as royal children. You can easily be fairly strict and very loving at the same time.
I have only read a page or two of the thread, so forgive me if this has already been addressed.
It seems to me that Henrik has always had an issue with his status and "place" in the Danish royal family. If I remember correctly, we went through something similar in the 1980's when P Frederick came of age.
There were tales of Henri's depression and his resentment that his son would now outshine the father as the heir. That Frederick would get the good assignments, etc.
That was some ten years or so ago (time flies). The trigger was the New Year Court for the diplomatic corps, where QMII was unable to attend due to a fall. So Frederik and PH went alone.
That's official business, so it was Frederik who, as Crown Prince and direct substitute for the Monarch, gave a speech to the diplomats and it was also Frederik the doyen among the diplomats directed his speech to. But when they lined up to receive the personal new year wishes from the diplomats it was PH who was senior, because now they wished the
family a Happy New Year.
In short PH was miffed because he felt
he should have given the speech, and that it was
him, the doyen should have addressed.
It was the final straw where PH felt (with some justification) that he had not been acknowledged by the public and the media. That the court administration didn't respect him (PH may think he is the patriarch, but constitutionally and administratively speaking QMII is in charge) and now his oldest son was usurping him - in public! So he felt humiliated and ran off to France.
And I have rarely seen a more toe-curling scene as the press meeting a few days later in France, where PH with QMII by his side assured that there were no problems and with Frederik and Joachim behind them. You didn't need a degree in body language to see F&J were embarrassed in that situation. - And a little while later PH was "promoted" to Prince Consort.