1) If your CMS just needs to be used in-house, then roll your own. It takes a week or less, you can deep-integrate it into your applications, and you'll be guaranteed to get more or less exactly what you want.
2) If you either need it to be exposed to external/non-technical people or you absolutely do not want to spend time developing CMS features, use WordPress for content pages and your app stack of choice for app pages. You can have them share the same domain if a requirement for e.g. SEO by using reverse proxy tricks -- trivial to Google if you know the words "reverse proxy." If not a requirement, don't do it that way.
One of the nice parts about using WordPress is if you have a high-generalizability problem like "It needs to work on an iPhone" then you are basically guaranteed that some 17 year old designer has hacked together a plugin which makes it mostly work on your iPhone. The downside of using WordPress is that... feel free to rephrase the last sentence.