Hej Maurits,
Hägg is a beautiful name, meaning bird cherry tree, and a popular name. Some has taken this name after birthplace, as the family you describe. There are over 70 places in Sweden in my atlas starting with Hägg- . Others has got it as a soldiers name. The online database for swedish soldiers under the old system can only show 50 hits, and when searching for soldiers named Hägg, not even all the ones with first names starting on A comes within these 50. Yet others have chosen it just because it is a nice name. The online phonebook has a limitation at 1000 - and there are more people named Hägg than this with a telephone in Sweden today. Over 1400 people named Hägg emigrated from Sweden in the late 1800s and early 1900s. I have been involved in research for an american Hägg/Hagg family - their grandfather, born Olsson, took this name at immigration, with inspiration from the name of his home farm in Sweden.
The origins, and the branches, of the family you describe may be correct, but not that they are connected to all the other Hägg in the world.
Best wishes,
Britt