If you want "yes" answers there's a narrative book-length study an Israeli feminist did on the question, with interviews of some mothers who regretted it. I've not found anything on fathers.
... and it's also worth noting that in the introduction of this book O. Donath, the author posts a typical example of one of the interesting death threats, wishes for her death, etc etc that she got from news reports of her original 2015 article that she expanded into the book