Actually it's not a problem in Europe only,. but all over the world. The reason is, that the booking system take into account, whether you are a Hilton Honors member or not, but not the membership level. So DIAs see the same rates as Gold or Silver members.

Maybe it's a good idea to show DIAs other prices for rates including executive lounge, breakfast of if the hotel has higher rates for two persons in a room.

The best way to avoid the additional costs is - as mentioned - to book the room for one person only. I never had any problem with that, no matter if I gave notice to the hotel before or not.

Btw: It's the 2nd person AND kids, who stay for free including breakfast. And from my point of view that makes much sense. I stay at hotels alone most of the times. Much less times I travel with my wife. And only a very few times I travel with my kids. But the stays with my family are much more important for my loyalty to a hotel group than when traveling alone. And from my experience Hilton Honors is really good especially at that point. My wife and my kids always enjoyed their stays very much.