Didn't they split up because he cheated on her with a model shortly after their baby was born? I know it wasn't explicitly stated but shortly after they split he was pictured a lot with a blonde model.
It's assuming a lot to say that because Dannii has a career that her ex does the bulk of the childcare.
The blonde model you refer to is Jennifer Hawkins, she works for the same agency as Smith (she is engaged).
Neither Dannii nor Kris have ever stated infidelity as the cause of the split.