Since the Emperor already knows about the relationship between Ling Mountain, Ling Hua, and Xiao Zhen, there's naturally no need for Ye Rui to keep it hidden upon arriving in the Capital.
So, after entering the city gates, Ye Rui planned to follow Xiao Jin's method, first entering the Imperial Palace to pay respects to the Emperor and Empress Dowager, then visiting the Crown Prince Residence to see Xiao Zhen, and finally going to the Marquis Residence. From top to bottom, rightfully so. Otherwise, bypassing the Emperor, Empress Dowager, and Crown Prince to meet Ling Hua first wouldn't be appropriate and could give the court officials something against him and Ling Hua.
Although Ling Mountain is not afraid of being impeached by the Imperial Censorate, it's always good to minimize troubles for Ling Hua.