Is Papa loyal to the king?

Yes, Annemarie's father is completely loyal to King Christian.

Papa thought for a moment. He always considered questions very carefully before he answered them . "Yes," he said at last. "It is true. Any Danish citizen would die for King Christian, to protect him ."

Papa's loyalty is also confirmed when Annemarie questions him about King Christian's inability to keep the Nazi's out of Denmark. From the text:

Papa sighed. "We are such a tiny country," he said. "And they are such an enormous enemy. Our king was wise. He knew how few soldiers Denmark had. He knew that many, many Danish people would die if we fought."