This answer is largely based on the article Fernando Zialcita, "Nick Joaquin: a portrait of the existentialist as Filipino", World Englishes 9(2) (1990), pp. 215-223. I haven't read "The Woman who had Two Navels" myself.
Firstly, there is an external or "out of universe" perspective of what the two navels can be seen as symbolising in Joaquin's story. This is explored by Josefina D. Constantino in a book chapter "Illusion and Reality in Nick Joaquin", pp. 13-14 in Joseph A. Galdon, ed., Philippine Fiction, Ateneo de Manila University Press, Quezon City, 1972. The following summary is quoted from the Zialcita article, as I haven't been able to access the Constantino chapter directly:
the two navels as symbolic of several things:
- Life’s two universes, illusion and fact,
- of evil and good,
- of Connie’s two existences: her childhood world of supposed innocence and her adult world of confusion and eventual regeneration.
On the other hand, a phenomenological approach, from Connie's own perspective, offers (according to Zialcita) an alternative three interpretations of the two navels:
Connie grew up during the 1930s when Manila still had an annual carnival. The merry-making had, as an emblem of luck, a Chinese deity, Biliken, who had a perpetual grin, long ears, and a fat, naked belly. Since her father, Manolo, was a carnival director she insisted on having a copy of the idol made for their garden. There she spent afternoons sharing tea and cookies with her toy. Returning to her ancestral home after the war, she finds the place in ruins and her Biliken on its back, with two bullet holes through the
Biliken thus suggests a childhood, an innocence and peace which she, in her current distress, wants to regain. Indeed, a week after she discovers the letters, on the day she cracks up, she finds herself driving back to Biliken in what is the begining of a new habit.
The two navels also symbolize her lack of personal autonomy. She dreams that she is her mother but also still herself. “I didn’t know which one I really was. I had somehow become both of us” (Joaquin, ca 1972: 95). And when she is woken up by her husband moving beside her, she suddenly believes that the two navels were there.
Bewildered about her sources and her goals in life, Connie sees her body’s center as not one but two. Connie’s portrait is that of a schizophrenic. The boundaries of her self-experience are vague and indeterminate. At one moment, she identifies herself with Biliken; her trauma has caused such severe distress that she finds herself drawn in two directions-on the one hand, she wants to be rid of her obsession (she asks Pepe for an operation); on the other, she clings to the obsession, for this allows her to withdraw from life by refusing to choose: "You see, I had made up my mind to be bad, to be wicked. But now I had been marked out, cut off from
everybody, like a leper. I had been saved from myself" (Joaquin, ca 1972: 95).
So there's many possible things that the two navels could represent: nostalgia for the idol Biliken (with its two belly holes like her two navels), Connie's lack of autonomy from her mother (the navel, in any human, represents one's tie to one's mother), and her schizophrenia (two body centre points instead of one).