The separation of personal and public life is something that is supposed to be apparent in all political forums. This seems to be so rarely the case when we see infidelity, gambling and other personal vices affect political motivations of leaders across the world. So if the negative aspects of a politicians life can affect their work life how much more could an emotional event like the death of a spouse affect the rulings of a political leader?
It truly comes down to the politician in question I think as grieving the loss of a loved one varies so much. Some people mourn privately and hide their pain and feelings from the world. In this type of politician I think you would see an increased effort to perform their tasks as thought nothing was different. For those that process their emotions in a more outward fashion the effect on their political decisions would be much more obvious. Depending on the death being due to illness or some other event such as murder or a car accident it seems as though you could expect those who process their mourning externally to start supporting political causes to help eliminate the cause of death in their loved one.