@Marshall5FD8 You have some good advice from others here already and I'll jump in to say that yes, InDesign is the right program for book production. It has a rather steep learning curve but for simple book projects you should be able to get the hang of the basic tools in a reasonable amount of time if you tend to learn software easily. There are many great online manuals and tutorials that are free.
Now, you might be able to achieve what you want to do with Acrobat alone. It depends on how extensive the changes are and what you plan to do with the book once you get it reworked. Sometimes it can be a nightmare to reflow text in Acrobat properly from page to page if you are inserting more than a few words in a paragraph. But if you want to proceed with InDesign, here are the steps I recommend.
The first thing you want to do is get the text from your sister's original book into an editable manuscript form so you can make your changes and then style the text with InDesign. When you scanned the book pages, you had a choice to scan to either text or pictures. I hope you chose the former! Most scanners render text into a PDF. From the PDF, you'll need to export the text to a Word document (or Rich Text format). If you have Word, then that's the best way to go. Clean up all your scanned and converted text in Word first. Make your edits and remove extra spaces, characters and so on. Make sure you've retained any italics or boldface. I like to convert all text in Word to one font (i.e., Times New Roman) and then apply individual fonts in InDesign. Run spell check and have the text proofread again unless you are only making a few simple changes. The less text editing you do in InDesign, the better.
In InDesign, set up your document with the trim size and an estimated number of pages (you can always add or delete pages later) that you want the final book to be PLUS A .125 inch BLEED all around if this is to be prepared for print. Typically, page counts in multiples of 16 are recommended (called signatures) for press efficiency or extra blank pages will be added to the end of the book to compensate in binding. You can have a half signature of 8 pages as well. Also, the book's front/back cover and spine are designed in a separate InDesign document that has to be calculated based on the final page count so the spine width is correct. You'll also need to consider the inside margins based on the number of pages so that text doesn't fall too close to the center of the spread.
Next, you want to import ("place") your text into InDesign. This is done through mapping or you can sometimes drag and drop the text and get great results. There are plenty of posts here about how to get your Word document ready for importing into InDesign. From this point, you can now work with all the tools to create styles for headlines and text. I hope this is helpful. Please let us know if you have any questions along the way as you go!