This is what... the 3rd time in 3 months Queen Margrethe has stepped in as regent since abdicating? Please correct me if I'm wrong.
King Frederik's vacationing seems a bit excessive to me, but I don't know Denmark's culture and relationship with their monarch - they may not even care.
We don't care, because it's normal. The school winter holiday is always in week #7 and many families go on vacation during that week. Many people take time off during the three days before Easter, especially if they have children and as such get an extended week of holiday. I'd say about a third of my colleagues are taking off next week.
Family time is very much a priority here. So in that respect FX&QM are seen as normal parents but also as model-parents because they prioritize their family-life.
And as their lives has changed quite a bit since they the Regent Couple, it's also seen as a good thing that they are aware and careful about giving their children attention especially the twins during the often tumultuous teen-years.
As we all know, you can give your children gifts and all sorts of stuff but what they really treasure is quality time with their parents (or anyone else who truly care for them).
King Frederik has also made it very clear that family-time is a priority. Period!
All Danish employees are by law entitled to 25 days of paid holidays and you are are expected to use them, otherwise you may risk losing them altogether. The money allocated to these holidays are paid by the employer and constitute the equivalent of 12½ % of your salary
On top of that after a certain period of employment most (today de facto all) employees are entitled to five additional paid days off. They were originally intended as days to be used for doctors appointments, visiting the vet, the "car's first sick-day" and other things where you would otherwise take a day off. But as so much is done online nowadays most use several of these five days for periods when things are say a little quiet at work.
Apart from that there is a mandatory employer-paid disposal account that is the equivalent of 7-11% of your salary (it depend on the type of employment) which cover holidays that fall on a weekday (During Easter that's three days covered by this account.) which means you get your normal salary these days. - Once there holidays are covered, you can use the money for whatever you want: Convert them into additional days off, or use them for your retirement fund or have them paid out to you. By next year that will roughly constitute an additional months of extra salary after taxes for most.
If you have children under the age of 14 and have been employed for a given period you are usually entitled to have the first day off, when you child falls ill. There are a multitude of rules and they may have changed since our children were that young. These days off (within reason of course) are either fully paid or constitute 80% of your salary. - The reason is of course to ensure that future taxpayers are produced in sufficient numbers... The practical reason for the parents is to ensure that they can find time to get someone to look after their child the next days.
All that is to illustrate that family-time is important in DK. As in: I can't find anyone to work for me-important!
In return you get some serious work done, when you are on the job and you also work, even if there are no one to check on you, also at the lowest levels. In fact we prefer not having anyone to check on us, they are in the way and prevent us from getting the work done.
So in that context FX&QM are not taking much time off. The criticism that King Frederik sometimes got when he was a CP was about the amount of work he (seemingly) did or didn't do between holidays, not the holidays he went on.