How would it look, if you inserted a blank page infront of the first page on the remaining chapters?
I think that's the way it's supposed to work when you export with spreads. Even though InDesign is coordinating the documents that make up each book chapter, they are still different documents that begin and end with a single page, so that's what comes out in the PDF. There might be a solution, but I can offer you something that will get you what you want, but not in a single step. For this example, let's assume that you have a 64-page book with four 16-page chapters.
- Make an additional document with the dimentions of a full spread as a single page (like a 17x11 doc if your book is 8.5x11).
- On the first page of that document, use File>Place, tick the Show Import Options in the Place window, navigate to the first chapter of your book, select page 16 and place it at the top left corner.
- Also on the first page, do the same with the second document, but place page 17 (it will show as page one in the window) to the right of page 16.
- Repeat for any other spreads of last and first pages.
- Save that doc and export it to PDF
- In Acrobat, replace the single pages from the book PDF with the spreads from the new PDF.
You will have to do this each time you export to PDF, but because the pages you place into the additional InDesign document will be linked to the pages from your book files, you will only need to be sure to update them in the Links Manager. In the old days, you would have had to export the book files as images (eps or pdf), but InDesign saves you that step by letting you place actual InDesign files as images.
Like I said, not one step, but still not too much extra work.