The QueenBee adored Claus and he once said something like she was the most intelligent, interesting and exciting person he had ever met. So there is that. Were they happy? With each other yes, I simply believe that Claus felt extremely useless in his life ( a bit like La Dame, though of course he was too fine a gentleman to throw a tantrum, it might however attributed to his illness).
Fabiola and Baudouin (I never get the spelling right, sorry) also were deeply in love with each other, but I think that their childlessness cast a very dark spell over their lives. I believe that they were able to rise above this, but it must have darkened their happiness.
I think that basically all of the relationships of the regent Queens with their consorts were somewhat troubled. At their time, men simply ruled the roost and those very handsome and distinguished gentlemen (Claus, Philip and Henry) had every reason to believe that they would be very successful and the catch of the crop. They actually made the most envied marriages and ended up passing the proverbial trousers to their wives, which must have been very difficult for men of that generation.
Claus made some snide remarks about his job of cutting ribbons (a far cry from the influential diplomat he had trained to become), Henry's tantrums are legend, and Philipp looked for adulation in the pursuit of beautiful socialites.