Sword Saint Meng had little care about the greater good of mankind or anything of the sort. What really mattered to her was just those whom she cared about, and if anyone dared to hurt her precious child, she would pit her life against that person.
The reason she had eventually relented was due to those words reassuring her.
As a mother, it was inevitable that she would bear great ambitions for her child's future. With Yang shi volunteering to assist in the process and her husband reassuring all of her fears, she had eventually caved in.
Otherwise, given her strength, no matter how powerful Hu Yiwei was, there was no way he could possibly have planted the Innate Fetal Poison in her successfully.