Though she has fourteen children, Kempe's role as mother is not the focus of her narrative. We only hear about one of her sons, who is described as a "tall young man." He goes into business and falls into the sin of lechery while abroad.
Although Junior behaves immorally with those bad women on the Continent, he too has a conversion experience prompted by illness. He becomes close to his mother spiritually, marries a nice German girl, and has a daughter. When Kempe witnesses the change in him, she decides it's time to tell her story:
[...] she opened her heart to him, showing and informing him how our Lord had drawn her through his mercy and by what means, and also how much grace he had shown her, which he said he was unworthy to hear. (II.2.268)
Within a page, Junior's dead. It's possible that the only reason his story makes it into the narrative at all is to explain the production history of Kempe's text.
That's right: Kempe's tall son may very well be the lousy first scribe who couldn't write well in German or English and made it nearly impossible for Scribe #2 to decipher the text. We're told at the beginning of Book II that "[...] our Sovereign Saviour had taken to his manifold mercy the person who first wrote the said treatise [...]," and then we're given the sad story of her young man.
Be that as it may, we're at least given a tiny glimpse of Kempe's interaction with her own child. It helps us to know Kempe in "homely" terms, as we watch her pray for her son and humblebrag about her "beautiful girl" grandchild.