Which families are you talking about? You have the Bourbon family in Spain and a cadet branch in Luxembourg, the Windsor family in the UK, the Glucksburg family in Denmark and Norway, the Bernadotte family in Sweden, the Saxe-Coburg and Gotha family in Belgium, the Liechtenstein family in Liechtenstein and the house of Orange-Nassau in the Netherlands.
How did they gain power? Through marriage politics and succession wars. But by no means is it just two or three families.