Parts in quotation from the blog of Trond Norén Isaksen http://trondni.blogspot.com
" The relationship between the two brothers had apparently never been very close, but it was the new Act of Succession which damaged it beyond repair...according to Count Ingolf, things “went completely wrong” when his younger brother was born in 1942 and the parents chose the name Christian, which would have been the name of the son Frederik “had counted on having”.
Since Queen Ingrid had trouble conceiving and difficult pregnancies, she was advised to have no more children after her 3rd daughter. Knud was thus created 'Heir to the Throne'.
The government had attempted previously to update the constitution (of 1915) but it had a low turnout so it wasn't approved without the needed majority. The WW2 years further postponed the issue but it was brought up again afterwards and this time with a new Act of Succession (perhaps it was felt this would bring attention to the larger issues?) and the debate quickly came to center on the issue of the 'choice' between the respective families. The press was pretty brutal in their comparisons (strapping King, attractive Queen, 3 lovely daughters) and the plainer (some called ugly) family of Knud & Caroline Mathilde. " Knud apparently blamed his sister-in-law Queen Ingrid for the change even though the changes weren't suggested by the King. (Though Ingrid did later write a letter of thanks to the politician who suggested the change). Count Ingolf admits he was disappointed, but adds: “One has of course gotten used to it. Said okay, that is obviously how life is meant to be. Then one just has to go on in a different way”. Count Ingolf points out that it was a much harder blow for his father, who “lived with the awareness throughout a long life”
Prime Minister Erik Eriksen later told the historian Tage Kaarsted that the Prince during the State Council itself had tried to sabotage the signing of the constitution. The two brothers hardly ever spoke again--and then only at official events. “I think my parents only saw King Frederik and Queen Ingrid when they met at official functions”, Count Ingolf says, “except for my 21st birthday, when I was to receive the Order of the Elephant from King Frederik because I had come of age. It happened during a lunch at my parents’ at Sorgenfri [Palace], but then they did of course have a reason!”
According to Ingolf, Knud never got over his bitterness for the few years that he outlived his brother and would've preferred to have spent those years, few that they were, as monarch. Perhaps to highlight the difference of what may have been, he left explicit instructions to have a quiet funeral. Ingolf decided that a decade plus of bitterness was enough and approached his cousin about a rapprochement (to the initial displeasure of his mother). "Ingolf “did simply not find it right that the older generation’s problems should continue to bother us. We of the next generation were not to have our lives ruined because our parents could not get along [...]”.
Count Ingolf, who lost his royal title when he married a commoner in 1968, annually receives 1.5 million DKK from the civil list as some sort of “compensation” for losing the throne. The siblings are seen at larger family events but the relationship on the whole still doesn't seem particularly warm.