So the order of events would be: the "Power of Royalty" resides in the "Violet Mansion." Somehow it was moved. The mansion was given to Yukariko. Years later, Hayate ventures into the "Royal Garden" and finds it there. Soon after, Yukariko ventures in and steals it.
At first I thought it was in the Royal Garden then Yukariko stole it and brought it to the Violet Mansion or something. However, Isumi mentions how she thinks the coffin/power was in the mansion and guardians protected that power (possibly the 28th) but the power was somehow lost so they lost their purpose and the Violet Mansion was given to Yukariko as they thought she would take care of the building. Following this premise and Yukariko's age when she received the mansion (6 years old), the Power of Royalty must have been in the Violet Mansion's coffin before it was in the Royal Garden's when Hayata found it (since she's older than Hayate.)
If interested, this is my educated guess (from here on it's my own theory and not based on facts):
I think the person on the phone giving orders to Yozora is probably Himegami himself. He probably had some link or relationship with the 28th (as seen in their photo) maybe was close to him and learned about the Power of Royalty from him. He went back to the Violet Mansion long ago and to Secret Room to find clues or track the power and probably dropped his photo there. He tracked it to the Royal Garden teaming up with Mikado and Athena. Athena knew the power was stolen (without knowing it was Yukariko, she pondered if it was Hayate at first.) but she still had reasons to go back to the Royal Garden (to see if Ikusa Ayasaki was trapped inside.) And so Himegami still tries to access the Royal Garden leading him eventually to Hayate in the Violet Mansion (as he was the one that could open it before), which prompts him to order Yozora to retrieve the photograph. At the end and since neither him or Athena can open the path anymore, it is hinted by Yozora on the phone that they must find a new candidate to open the path (Ruka.) I still don't have a big theory/guess on the involvement of Aika other than that her butler/fiancee could be no other than... Himegami! But that's a wild guess.
So what do you guys think? Discuss discuss :D