Hi Cornelia,
Unfortunately, Adobe Photoshop Elements doesn't support the CMYK color space. This is one of the main distinguishing differences between Photoshop Elements (a consumer-oriented software application) and Adobe Photoshop CC (a professional-level software application). Don't get me wrong, Photoshop Elements can produce "professional-quality" work, hence its popularity, but there are certain advanced features which are purely the domain of Photoshop.
In a lot of cases now, print-on-demand services are quite used to receiving RGB files and include converting them to CMYK as part of their pre-press service. To be honest, IngramSpark appear to be following a very traditional old-style print workflow and for them to have to produce a 35-page heavy-going technical manual (PDF) covering their submission guidelines is ultimately going to scare off many potential customers.
Compare that with Lulu who have a much more modern print workflow and actually prefer RGB files which their printers will then automatically convert to CMYK. Their Book Creation Guide is a lot easier to read too 🙂
So you might want to reconsider your publisher of choice...
If not, then the best value option for subscribing to Adobe Photoshop CC, is the Adobe Creative Cloud Photography plan which is priced at $9.99 per month:
Adobe Creative Cloud Photography plan
You can also take advantage of a free, 7 day trial if you want to check it out first before committing yourself to a subscription. Just remember to cancel it before the 7 days are up, or you'll be automatically charged for a subscription!
Photography plan trial (it's the middle option)
Hope that helps 🙂