What is the best way to explain unrelated work in a Masters application?
It is unclear whether you are applying for a coursework Masters or a research Masters. If it is a research Masters, applying for a project that straddles across three disciplines seems unlikely (political science/international relations/public policy). 

Coursework Masters tend to not have a high selection process as coursework Masters tend to be funded by the student compared to a research Masters.

So if it is a research Masters that you are applying for, then evidence of the ability to do research would tend to be the focus. If you have done an honour thesis during your law degree, that would be significant useful. If you have done extensive research and wrote long form analysis as part of your role as a corporate lawyer, then that would be relevant too. Some lawyers have written submissions or in-house publications, so that would be good evidence of your work. 

Being able to show that you are able to engage with difficult political science and public policy issues would be useful as well.  You have done international relations in your undergrad but you may not be as convincing in the areas of political science and public policy especially at a research Masters level. Extra-curriculars would not be that convincing, unless it is extra-curriculars that has produced good work such as an editor of a student journal or publications that potential supervisors that are able to examine.