Yes, take a piece to either a lumber yard or a sider or even a cabinet maker. If you take it to a paint store, you may get the wrong 'diagnosis'. I'd even suggest you get a couple of opinions because sometimes even the experts aren't sure. In fact, ask them if they're 100% sure!
You can even take it to the Forestry department (or the like) at the local university. They can tell what the wood is by scraping a 'clear' edge, wetting it, and using a monocular to look at the cell structure! I know. My roommate was a Forest Biology major and this was known as the 'field test'. (... what you need to do when you don't have the luxury of a laboratory in the field.)
I'll bet the exterior was NOT primed with an oil based primer. If this is the case, well, you can get a few reasons why the primer/paint won't stick. If you need more, post up. When you have all your answers, please post a follow-up (SUCCESS!) and let us all know how you made out.