If the PM needs to babysit them in everything they do, then IMO that would mean that they are incapable of making any sound decisions themselves. I don't think that's they case, so they can analyze the situation, reflect further on their own behavior & do better from now on.
I don't think any of the other European royals went on vacation abroad this year? Not because they couldn't afford to or wouldn't be able to better protect themselves from infection than regular people, but because I imagine they realized that it wasn't a good time to do so. Not when citizens were asked not to or were suffering from illness & economic consequences.
I think they weren't even criticized when they went in the summer, it was when they went right after the PM had asked people not to, that they got into trouble.
It's a time of crisis and as such, I think their actions are amplified. If you rise to the occasion, it can be huge boost in positive perception that may even last for years - eg Philippe & family or Sofia of Sweden. Something as simple (but very meaningful & hitting just the right nerve) as "You are not alone" can make you shine greatly.
Willem-Alexander and Maxima messed up, and it also got a stronger reaction than it would have in a different situation. Now I think it is wise indeed to stay quiet for a while.
They seem to have to been incredibly popular and perhaps that has given them the idea that nothing could change that... Now they've seen that that isn't so and will hopefully do better in the future. Luckily, for them this is very much salvageable. Felipe would probably be done in such a scenario...