[Need Advice] Fixed Layout or Reflowable Layout?

The short answer is that fixed layout (FXL) is a complicated and difficult layout, largely obsolete. It should only be used for "picture page" books like illustration-based children's books, graphic novels, and the like. All other books that are all/mostly text or have illustrations through the text should use reflowable.

Your project is a children's book, which would seem to make it a candidate for FXL, but the problems multiply from there with multimedia elements, animation and the like. The truth is that EPUB is not a very good format overall, with a standard stuck a decade or more behind reality and zero enforced or de-facto oversight of the critical readers. As with other digital formats, EPUB is 100% dependent on the reader used, its compliance to standards and the scope of any variance, added features or "I can make this better" notions by the developer.

Complex EPUB books can be built and succeed on the most standards-based readers (Calibre, Thorium). But EPUB + FXL + animations etc. is going to be a bag of walnuts pretty much no matter what approach is used.

(There's an assumption, fueled by the prevalence of animation and multimedia in things like web pages and phone apps, that all such tech is mature and workable. There are, unfortunately, many platforms and standards for which modern notions of animation and interactivity never worked well and likely never will, and EPUB is one of those platforms.)

Reflowable will never work and you've discovered why fixed layout is essentially useless except in very limited cases. What reader app are you using to test this EPUB? The only ones I can even remotely recommend are Thorium Reader for Windows and the native Books app on Mac.