Plores

pluere = "to flow" + plorare = "to cry" (Latin)

"flow" suggested by "uncontrollable birth" (menstruation), and "cry" by contrast to "laughing" in the full line:

"laughing through all plores for us (her birth is uncontrollable)"

Of course, it's also a reference to Anna Livia Plurabelle, references to whom occur in the previous paragraph ("annaone," "you liv," and the sentence with many bird's names and descriptions beginning with "p"); and the sentence before "plores" includes "truetowife," followed by "livving."

(all plores = all fours?) (all plores = applause? public acclaim? the clap?)