So this could turn into a long winded answer if I go into all the lore background so I'll keep it brief.

Willows father is pretty much the right hand of the king, so there is a connection between his family and the royal family. Although there is some physical distance between his familys place and the royal court, he has spent enough time there. This connection is not the reason for Willow ending up as part of the kings guard though, Willow is just very determined and diligent in his training. There's also something more there but I don't want to spoil that XD

First off, Douglas and Willow are not from the same country. But Douglas as a leading figure of his own country has connections and he is a charming man when he wants. He is good friends with the king of a neighboring country and was invited to the court for diplomatic reasons. The King warms up to him easily enough.