King Augustus wanted to wake up Queen Titania, as his state was obviously not right. So he decided to enter his soul domain with just his spiritual form. It's okay for couples to enter each other's domain, but it will be almost impossible for strangers to let their souls roam, as any damage done in this place would reflect on the soul of the owner of the domain.
At this moment, Queen Titania had already closed off her heart before this happened. Adding to the fact that King Augustus and Queen Titania treated each other as just acquaintances, it would most likely be impossible for each other to enter their soul domain. Even so, King Augustus still wants to try doing so. The backlash of rejection of someone's soul domain is an injury to the soul. That's why Imperial Doctor Ruth and Imperial Healer Kane were against their king entering the soul domain of someone as powerful as Queen Titania.