It depends who is using the tree and what you want to document. I would add the step child and the new husband, even if your cousin does not have children with him. It does seem a bit improper to me to leave them out (or to include the husband and leave out his child) but people make family trees for different reasons.
This is probably not the only step-family in your tree. If you don't have any yet, you will later. It was very common for people to remarry when widowed. Divorce happened too. And death was not uncommon when young (in childbirth, in wars, disease, and accidents).
As for your cousin's pronouncement that she is not a step-mother, if the child is a minor, I hope she gets over that fast. But that has nothing to do with genealogy. The tree doesn't give her relationship to the child, just to the child's father. The rest is implied.