In Denmark, Margreth married a mere Count, the next sister Benedikte, a Prince and the youngest, Ann-Marie, a King !
I've learned that the late Prince Hendrik was not even bon to real nobility. Rather, he was a member of the faux nobility: the comital title was created for the Monzapat family. Evidently his father-in-law, King Frederik IX of Denmark, was unaware of the situation and thought that his future son-in-law was a genuine nobleman. It had to be a sore point later on for his nephews, whose marriages to commoners were unapproved, since *Count Henri* was actually technically one himself.
Did Ann-Marie outrank her sister Benedikte in Denmark ?
I don't believe so, anymore than Benedikte outranked HER older sister simply for being married to a prince whose house is listed in the second section of the ALMANACH DE GOTHA. Like I said, in reigning houses, rank depends on genealogical seniority -- as long as the marriages are all dynastically approved.
Interestingly enough, the problem with Anne-Marie's marriage was not the *equality* of her husband's birth (duh), as it was the fact that he was the heir-apparent to a foreign reigning house. The Danish constitution forbids the sovereign to be the king or queen of another country. So she forfeited her place in the line of succession to the throne of Denmark, on the occasion: as with the Dutch princesses (who, according to the constitution of the Netherlands, were not allowed to renounce their succession rights, but could nevertheless forfeit them by marrying without the consent of Parliament), I'm assuming that she didn't even seek her father's consent.
Speaking of the Dutch sisters: a similar situation could be observed of the daughter of the late Queen Juliana. The eldest, who succeeded her on the throne as Queen Beatrix, married only a minor German nobleman, Count Claus von Amsberg (born only a tad bit higher than Count Henri de Monzapat, who like I said was not really a member of the French nobility by birth; at least Claus was a genuine nobleman). By contrast, the second daughter married a royal prince of *equal* birth, who would eventually become head of the house of Bourbon-Parma. Of course, the two younger daughters (unlike Princess Anne-Marie of Denmark) married untitled commoners ...
So Princess Irene was the only daughter of her parents to make a royal marriage. Because she married without the consent of the Dutch parliament, the union is non-dynastic. By contrast, her sister Margriet retained her succession rights by seeking and receiving consent for her marriage. Her situation might be comparable to that of Princess Benedikte, who received consent for her marriage and has a place in the royal life of Denmark (although her children forfeited their places in the Danish succession by failing to reside in the country).
However, in international social circles, I believe Anne-Marie outranks Benedikte; and it's conceivable that Irene outranks her younger sisters.