If Ottawa's ebook lending system is anything like Vancouver's, for ePub books you download an ".acsm" file from their website. When you open that file using ADE, it appears in ADE as a DRMd ePub file. ADE will show how long the lending period is for, and allows you to "return" the book before the expiry period. If you have your Kobo or Sony connected to your computer when you start ADE, it will recognize the device and allow you to copy the ePub over to the device.
To read non-DRM ePubs on a Kindle, use Calibre (aka iTunes for ebooks), load your ebooks into calibre, and connect your Kindle to your computer. When you send an ePub to your Kindle Calibre will automatically convert to mobi format.