If A wanna give up her daughter because of that
man, she is being utterly foolish and stupid. Its not about values,
not about business-like-profit-minus-cost-become-damn-bo-hua - its
about she making her FIRST major mistake of having unprotected
pre-maritial sex with her ex-bf, who became her ex-husband due to
society standard/pressue/effect, where she decided psychologically,
emotionally and spiritually that she would want to raise the
child.
It would become her SECOND major mistake if she were to accept that
proposal.
Mentioned before by other forum mates - if he can't accept her
daughter, his love to her is very superficial.
Then how?
She can only wait to see if fate allows her to bring her a man who
sees her as herself and not of her status (divorced) &
possession (child) - if fate doesn't give her that, then her reward
would come from her daughter when she grows up, mature and
recongise the hardship that her mum took in exchange for this
happiness. 
P.S: Having that society-disapproved status DOES NOT MAKE HER ANY
LESSER/INFERIOR in terms of a love, therefore her mum's comments is
invalid. She has the right and authority to find and choose a guy
who appreciate, treasure and look beyond. In eyes of love, all is
equal. 
Cheers