Being forced to choose between imprisonment and compulsory sterilization is not "choice."
rightfully pointed out, it is immoral for the government to "make someone choose between reproductive freedom and the survival of their existing family." Advocating for such government intervention is not merely anti-choice, it borders on classist and racist, as well.
A person who neglects his/her children is punished by losing his/her custodial and parental rights, not by being thrown in jail. Depending on the level of abuse and various socioeconomic factors, prison time for the parent may be advisable. Suggesting first that we imprison parents with multiple "neglected" children is deeply disturbing. Suggesting second that we should offer state-sponsored sterilization as an alternative to jail time is coercive, invasive, and getting very close to eugenics.
The government has no place being the arbiter of who gets to bear children and who gets sterilized. There are no standards that could be employed by a government that wouldn't disproportionately target the already marginalized and disenfranchised sectors of society, as has been evidenced by the terrible history of forced sterilization in the United States.
The bottom line is that you are making seriously callous judgments on women's reproductive choices for the simple reason that they don't sync with yours. You are then trying to turn your bias into laws that strip women of their fertility. And that is not, under any circumstances, pro-choice.
On a side note, you can be pro-choice and childfree, but you can hardly be pro-choice and anti-motherhood.