If I understand your question correctly, you want the latter half of your booklet to essentially be upside down? If that is indeed the case, I see two options, each one with their respective downsides:
1) (this is the one I would do) Design the whole thing in Indesign, with everything right side up. This means that the pages of the 2nd half will be in reverse order in the InDesign document. When you are happy with the layout, manually rotate all the elements on each page in the second half of the booklet 180 degrees. Then, just export and print. This way, you only work in one document in one application, but you will have to layout the pages for the second half backwards (might take some getting used to).
Essentially, you will layout your pages as in the picture (only with 52 pages, obviously). The first half of pages (1 2 3 4) are laid out normally, then the next half is laid out in reverse order (4 3 2 1). Then, once you are done, rotate the content of the second half of pages 180 degrees.
EDIT: as per comment from @Yorik below, you can alternatively rotate the VIEW of the spreads, which enables you to work on the content the way it's supposed to look while in the exported PDF it will be upside down. The option is in the dropdown menu of the "pages" panel unter "Rotate Spread View".
In the picture, the first row of pages represents your original layout. The second row represents how your pages should look before exporting.
2) Create two InDesign files, one for each half. Order the pages in the normal order for both halves (the way they are supposed to be read). When you are done layouting, export both as PDF, and then for the 2nd half, turn all the pages 180 degrees in Acrobat Pro (I assume you have access to Acrobat Pro and all its related tools), manually reverse the order of the pages, and add them to the end of the PDF of the first half. Save and print. This way, you can layout both halves normally, without having to "think in reverse" for the 2nd half, but you will have to go through the same process of exporting 2 pdfs, flipping, reversing and inserting pages every time you make any change to the document.
In general, I prefer not to switch applications if at all possible, so I strongly recommend option 1, but both options work.
Addendum: this thread on the Adobe forums is really old, but contains potentially relevant advice: https://forums.adobe.com/thread/484334