A question I haven't seen brought up yet: what would be the consequences if the alleged affair is true? HRH The Crown Prince of Denmark isn't going to lose either his position or his wife because she's has too much invested both emotionally and politically to be reactionary to a dalliance. He may lose some reputation, but that will heal over time, especially if he remains as hardworking as he always has been. He may garner the disappointment of his mother and children, but that can heal too.
To give an earlier example, Charles III married his long-time mistress, and nearly 20 years later he and Queen Camilla are deeply beloved throughout their realms.
Ultimately, his infidelity or lack thereof is a private matter between him and his wife. As long as he continues to keep up his duties as crown prince, the public shouldn't be too hard on him.
Post script: Europeans are a lot more trusting of their partners than all of the Americans I know are. Even if they have been married for decades, many partners would be uncomfortable with their significant others staying overnight alone with friends of the opposite sex, and many of those significant others wouldn't do so because they would find it disrespectful to their partners.
That's a
very open question.
It depends very much on Mary's reaction and whether the two of them could work it out.
If Mary opts for a divorce or a de facto separation or just their relationship cools visibly, Frederik will be in deep trouble!
Frederik will have to work exceptionally hard and also have to use his people skills to the fullest and even then I doubt he will be able to recover.
Mary is crucial for Frederik, vital.
I dare say that to many Danes Mary is the best monarch we can't have. The second best thing is her as an (influential) queen consort.
Without Mary in the picture or even worse Mary as a competitor, I believe Frederik will struggle.
And the old ghost about suitability will surface again. From back when he was unfavorably compared to Joachim. (Not that Joachim will be involved this time, even though he may have to step in as a kind of mentor for Christian, in the worst case scenario where the relationship between Christian and Frederik go sour as well.)
I think there will be many a prayer
openly wishing for QMII to live beyond 100 so that Christian can take over.
In any way Frederik will get a very rough time. Danes are very direct and people will have no qualms about telling him to his face to be ashamed or just quit, when he is out and about.
The best scenario is that he and Mary are open about this and it happened and they are working together to mend things.
Frederik will still get some serious heat, but should they even manage to reconcile and even find their old spark, Frederik will get a more lenient treatment - and Mary will be elevated to saint!
In contrast to King Charles, - who has been working hard to rebuild his reputation from an already loveless marriage that should never have taken place, from a marriage that was already broken down and where both sides must be said to share at least some of the blame, - I can't see Frederik will be able to recover to anywhere the full extent of the standing he has now.
Having said that I still don't believe in an affair. I think (based on his portraits) that Frederik is a very informal guest when visiting his friends, who has no problems sleeping on the couch. Royal or not. And that his friends know that and are used to that.
Also, while PET will normally follow him around, there are times when he - and other members of the DRF go without PET protection. The details have never been disclosed but I imagine it can be at times where he is under the radar. Like going for a ride on cycle during an unannounced weekend at Trend. I am however surprised that he should go to Spain or any other country, without being followed by PET - or more likely Spanish security.
PET can deny permission for people who are under protection for a specific threat to do certain things - or they pull their protection. But it's a little more fluent in regards to those who have and must have permanent protection. Here I imagine there is sometimes some bargaining taking place.
Had this taken place in Copenhagen, PET would simply wait all night on the street, I'm certain of that.
But what Spanish police may do if Frederik dismiss them is not something I feel I can say anything about.
I don't believe Frederik would be able to sneak into Spain incognito. I.e. unannounced using a "fake" passport (the name Hansen BTW). At the very least PET would inform their Spanish counterpart.
It would equally be improbable for Frederik to sneak off to the airport and fly off to Spain. Because after a few hours at most the officers on duty will wonder where he is and the alarm bells will sound all over the country!
And when they figure out he has boarded a plane for Spain, Spanish security will be alerted. - That's an extremely far out scenario and I only mention it because everything that is not totally improbable is a possibility.