I'm surprised this hasn't been mentioned before...but what if the Garden of Amahara is supposed to represent the Garden of Eden?
After all, anyone familiar with the story (and all the versions: Judaism, Christianity, and Islam, though most notably I think the Christianity version would have been considered) knows how related it is to Satan. This could explain a possible connection between Sheimi and the twins.
Taking a passage from Genesis:
Now the serpent was more crafty than any of the wild animals the LORD God had made. He said to the woman, “Did God really say, ‘You must not eat from any tree in the garden’?” The woman said to the serpent, “We may eat fruit from the trees in the garden, but God did say, ‘You must not eat fruit from the tree that is in the middle of the garden, and you must not touch it, or you will die.’" “You will not certainly die,” the serpent said to the woman. “For God knows that when you eat from it your eyes will be opened, and you will be like God, knowing good and evil.” When the woman saw that the fruit of the tree was good for food and pleasing to the eye, and also desirable for gaining wisdom, she took some and ate it. She also gave some to her husband, who was with her, and he ate it. Then the eyes of both of them were opened, and they realized they were naked; so they sewed fig leaves together and made coverings for themselves.
Notice that there's a big theme of good and evil here. This theme is very prominent in the manga. After all, we have characters -- notably, Yukio -- who speculate all the time about what is good and what is evil. Supposedly, the fruit of the trees in the Garden of Eden hold this knowledge. Therefore, the Garden of Amahara -- while "legend" to Sheimi -- might actually hold answers to what good and evil are, and what the solutions might be. It might have connections to the Blue Knight, and to the truth everyone seeks. Even if the garden itself isn't real, it might be symbolic of other connections to Shemihaza...like Sheimi.
We know that Shemihaza has pretty obvious connections to Sheimi. After all, Sheimi's name is similar to "Shemihaza," and they both have the motif of gardens, etc. etc.
From the Emperors thread:
Shemihaza is the leader of the Grigori, which makes sense since Shemihaza was also the name of the leader of a band of fallen angels in the Book of Enoch from which it was inspired. His title is the Emperor of Creation, which implies that he had some sort of part in the making of the world. His motif is plants, which goes well with his title.
So..."Shemihaza" is the name of a leader of a band of fallen angels. And the Garden of Eden is a garden, which is connected to creation, which is connected to Shemihaza. And Satan was a fallen angel, who tempted Eve (Adam in Islam's version) and got them kicked out of the Garden. There's a lot of intertwining with the story here, between fallen angels, Satan, gardens and creation. And all this has got to be tied to Sheimi, somehow. More particularly, to Sheimi and Satan. Her family clearly has some sort of history with Shemihaza, one that Sheimi doesn't know about...she doesn't need to know about it, necessarily, because it's so far back, I'm guessing, but it must connect with this entire thing about demons, thus influencing her decision to become an Exorcist.
Shemihaza is on the side of humans. This makes sense if she/he/it has connections to the Garden of Amahara (Eden). If Satan is anti-human and caused Adam and Eve, or "humans," to be kicked out of the Garden, Shemihaza might be against that having happened, and is thus there to protect humans, or bring them back onto better terms with "God," or just bring them back into the garden, or "peace."
Either this, or the Garden of Amahara can simply represent the Gardens in heaven, which I think has been mentioned before. But that doesn't leave much room for speculation, does it?