Well the parent and step parent should talk about how the parent wants to raise the child and how they feel about punishment so if there is a time that the step parent is left in charge there won't be any disagreemets about how the child was cared for but if the parent is home and sees what the child is doing the parent should do the punisment so the step parent doesn't always look like the bad person. I think it should be 50/50 as if it was to be both parents so the child doesn't try to take control of one or the other
I don't have children, but I would hope that for both people- when a step parent is introduced; the 'step' no only loves the child as he/she would their own, but knows exactly the expectations the parent wants/expects in fromt of the child. When marrying someone with a child, you have to understand th child is of your spouses' blood and love them as so.
I don't think the step parent should have any power at first. I think the power should be gradual and 50/50 amongst the parents. I think the step parent should be able to put some input on how the child is raised so that when the child is disciplined by either parent it is consist.