Alright, I'll try to give a somewhat decent answer to this, though I'm far from an expert on monarchies. The point is, most nations (with a few exceptions like Venice) had been ruled by a king for a long time, sometimes literally thousands of years. People had simply gotten used to it, and experiments towards republicanism weren't always successful. The best example of this is of course the French revolution, which eventually ended with the Bourbon restoration due to foreign monarchies sensing the threat posed by republicanism. Besides that, what was the alternative? A lot of 'democratic' ideas were only formulated fairly late, and even then radical new ideas usually take some time to sink in. Combine that with slow communication and transport plus the generally low level of education, and democracy really wasn't an option (at least in the 18th century, technology improved in the 19th). Another factor we can't forget is that people were quite religious in those days, and kings were ordained by God. That would have been a deterrent, along with the massive military forces kings could call upon to defend their throne.
As for the familial ties between royal houses: I'm not sure whether this was a problem in the period you described, but it did play up in WWI. The royal houses of the UK and Belgium (both Von Saxen-Coburg-Gotha originally) did sever their connection to Germany. The British royals gave up their German titles (Duke of Hannover, etc.) and name after the Germans constructed their famous bomber plane, the Gotha IV (you can see the connection with the royal name). They became the house of Windsor. The Belgian royals changed their official name to 'of Belgium'. That's about what I could draw out of my head, if anyone else has a better knowledge on the subject, I welcome their contribution.