Arabella once thought that Lucille was the most mature among them, but apparently not.
As requested by Rendell, Julia called for the one in charge of security. It was the Vice-Commander of their Knights. Rendell had a conversation with the Vice-Commander using a magic tool to prevent their talk from being heard and revealing the security layout.
When Rendell and the Vice-Commander shook hands, it was clear the conversation went well. Rendell then agreed for Arabella to attend.
In matters related to her safety, as her personal guard assigned by Ferdinand, Rendell was allowed to decide things for her to ensure her safety. Once Rendell believes her security was in jeopardy, he was allowed break in and take her to safety even in the midst of the Assembly.
Those were rules Ferdinand had reiterated before they departed for Medeus.
If Ferdinand wasn't with her to ensure her safety himself; Rendell, Alwin, and Riley may decide on what to do in case there was danger.