What kind of fantasy world is it where the "dad's wife" of children, with whom there is shared custody or even regular visitation, is 'nothing to do' with parenting???
Does she have to change her schedule or her lifestyle because there are children's needs to consider? Damn straight she does.
Does any part of her or her partner's finances go to caring for the children? I should think so!
Does she have to live with (even on a part-time basis) the personalities and foibles of the children, with no option to simply walk away? Almost certainly!
Does she share other family members with the children in question - in-laws, other kids, etc? Quite possibly.
Even the least involved step-parents of dependent children end up HAVING NO CHOICE but to take on at least some of the tasks of parenting. The label step-parent reflects that.
I love my stepkids. But even if I didn't (and even when we don't like one another very much), I STILL have to make sure they are fed and clothed and well. I still have to take an interest in their manners, their discipline, and their education. I still have to consider them in every decision I make - where to go on holiday, where to live, where to retire, what to serve for dinner, what to do on a friday night, how loudly to play my stereo, what jobs to apply for, whether to have more kids...
I'm their stepmother, whether any of us like the term or not.