I'm laying out a book. Each chapter has facing pages, with inner/outer margins. I'd like the chapters to start on odd or even pages, whichever is next. But my margins wind up on the wrong side for even chapters.

I’m new to InDesign, but have made books in other products. I have chapters all made with the same template and parent settings. I put them in a book. I want the chapters to start on odd or even pages, depending on how the chapters lay out. The chapters that start on odd pages look great. But the ones that start on even pages have the inner and outer margins backwards. Is there a way to set up my parents so a chapter will have the margin (and page headers and the like) be correct for whether it winds up starting on the right or the left? (So that if I add a page, say, to an early chapter, the change ripples correctly through the rest of the chapters.) I’ve attached my first test case with four chapters. Note the third one, “Illness and Injuries” starts on the left, but the margins are set for a right side page. Thanks in advance.