The Default Events Template is really the “standard” for displaying events – Default Page Template (and others, depending on what your theme makes available) are really just to present some alternatives in the case of theme conflicts etc.
In this instance it would probably be easiest to add your sidebar by customizing the Default Events Template – and we’ve got some great learning resources to get you on track for doing just that, starting with our Themer’s Guide 🙂
Hope that helps!