Is it possible to make bookshelves in the library contain skill books? In Barnacle Bay and Hidden Springs libraries I have the regular books and the children books only.

Yup, you'll need to edit the library in edit town. Either add in extra skill book bookshelves (either the Book Corral or the Penningway Bookshelf) somewhere on the lot, or use this mod to set the existing bookshelves to include skill books.