For those who believe mom should not use "dad's" last name after divorce maybe because others will think she is still married to him, think she somehow acts like she is still married to him, or because you or your husband just hate it or don't want to be associated with her in that way -
What about if mom doesn't want you taking your husband's last name because it is the same as her kids? What if she doesn't want people thinking you're her kids mom or thinks you'll act or think like their mom because people assume that a woman with a kids last name is mom a lot of the time if mom isn't known. Maybe she just doesn't want you associated with her kids at all.
Would you care that it bothered her? Or would you expect her to just deal with you changing your last name to a different one?
Because, let's be honest, it is a lot easier to pull some crappy stunts when you have the same last name as a minor in your care/your husband's care than it is as an adult to pass herself off as the wife of someone.