Can I sell a PDF through the iBooks store? I want to sell my children's books on Apple.  They are ready because I made them all on Corel. Is there a possibility of turning them into PDF and publishing them in that format or will I have to do it all again on iBooks Author?
Apple has a support document that addresses this very topic:  Publish and sell books with iBooks Author


If you intend to put your books up for sale on the Apple Book Store, then they must be in the iBooks (.ibooks) or EPUB (.epub) format.  You will have to use iBooks Author for .ibooks.  For .epub you can use iBA, Pages, or various other apps.
If you intend to have a wider distribution outside of iBooks, then they must be in a different format than iBooks like PDF or EPUB.  If you go this route, you don't need to use iBooks Author; you can use the PDFs generated in Corel. One vendor for this is gumroad - https://gumroad.com/