The way you phrased your question implies that you’re asking about a sorts-of-permanent disguising as a woman (which, in effect, would mean to live as a woman). That I am not aware of ever having happened (for one, since there's only one royal family, who are these enemies?).

What I can think of is the following:

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The Heiji monogatari, a historical tale about a clash of powers within the imperial court in the year 1159/1160, narrates that “Emperor Nijō, for his part, had a carriage brought up to the north gate and dressed as a gentlewoman wearing layered robes” to secure his escape from the imperial palace to a safer location before the outbreak of hostilities (1). When the carriage was examined by a group of warriors belonging to the coup faction, it is said that:

Emperor Nijō, then in his seventeenth year, had only recently acceded to the throne. His face still had the fresh beauty of youth, and, colorfully dressed as he was, he did indeed resemble a dazzlingly beautiful gentlewoman. They let the carriage pass without further ado. (2)

Incidentally, Retired Emperor Goshirakawa merely disguised as regular nobleman (Tyler speaks of a "privy gentleman") during his own escape.

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Similarly, the late-13th century chronicle Azuma kagami relates the attempted escape of Minamoto no Yoshitaka, a 12-year-old boy and son of Yoritomo's cousin Yoshinaka from Kamakura, seat of Minamoto no Yoritomo, the soon-to-be first shogun. Yoshitaka was, for one, a hostage (a sign of trust); and also promised to Yoritomo’s daughter Ōhime.

However, when the uneasy alliance between Yoritomo and Yoshinaka broke apart after Yoshinaka occupied the capital of Kyoto, Yoritomo decided that the boy, which apparently was promised to his daughter for marriage, were to be executed. An attempt to smuggle the boy out of the city disguised as a female servant, which was arranged by Yoritomo’s wife and daughter, was unsuccessful, and the boy paid with his life (3).

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Hence, the idea of disguising as a woman (or, simply, as a person of different social status, as with Goshirakawa) was certainly not unheard of. However, these actions were, so-to-speak, emergency measures, and not of a permanent nature. What such anecdotes can show are historical attitudes about the relationship between clothing, the body, and gender (just think about how the Heiji monogatari implies that the disguise, in part, was effective because the emperor’s facial features were youthful).

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Notes:

(1) The conflict was more precisely between the lay monk Shinsei, who guided court politics at the time with the support of Retired Emperor Goshirakawa and the top-ranked courtier Fujiwara no Nobuyori, who allied with a faction interested in direct rule by the new emperor, Nijō, instead of Goshirakawa. Neither of the imperial family were targets per se (the intent rather was to keep them under control in a location under one's own control), although it cannot be excluded that something would happen if the palace were to be assaulted and set on fire. Although Shinsei would not survive this conflict, the Taira forces supporting him and Goshirakawa ultimately managed to defeat the rebellious faction, whose ringleaders all paid with their lives.

(2) This and the preceding quotation are taken from Royall Tyler’s translation published in Before Heike and After: Hōgen, Heiji, Jōkyūki, pg. 127 and 128, respectively.

(3) Azuma kagami, entries for Genryaku 1 (1184) 4/21 to 4/26. I don't have them at hand right now, so this summary has to suffice.