Unpleasant but with all scheming to get the throne this practice is somewhat understandable. It is to ensure legitimate bloodline. I think it had been implemented in real life as well.
Hazel found it to be weird how there would be days assigned for her to sleep with Tobias. Why did anyone have to know when they were being intimate? The whole palace was going to know and then maybe the town would too. Why couldn't the matter be private since they both knew they were to try for a child?