Learn English – Gender-independent replacement for “fiancée” and “fiancé”

Use her name - in the UK, there is no expression you could possibly use that would not be considered insultingly paternalistic (if used by a man), over familiar, patronising or chauvinistic. In previous times, terms such as 'dear' 'love' 'duckie' 'sweetie' 'sugar' and even darling might have been used - none would be considered acceptable today in the circumstances you describe.

Though I am disgusted at the Greek-Latin lexical miscegenation, a parent of multiple children is polyprogenitive, from the Latin prōgeniēs, 'to beget'. From The Embodied Female:

Co-wives and surrogacy exist since Biblical times. For instance, resenting the four sons her fertile sister “gave” their common husband Jacob, barren Rachel gives him her maid Bilhah as surrogate, and adopts the two sons by this union. Emotions driving these transactions are unaccounted by Freudian chains of phallocentric symbolic equations slip-sliding between baby = penis or Darwinian notions of polyprogenitive male desire to spread his sperm. Neither can egg-exchange be entirely construed by Kleinian gynaecratic accounts of reparative urges to undo unconscious phantasies of raiding the archaic mother's envied fertile body for the babies within.

Technically, and although it doesn't fit the poly- mold requested, a person with more than one child would be multiprogenic (or multi-progenic). (The Greek equivalent, as Janus pointed out, is polytecnic, from τέκνον meaning 'child, son'.)

Similarly, a person who has children with multiple partners, according to social scientists, practices multipartnered fertility.