One Installation, use different theme on different, categories, tags and pages

Yes and NO,

You can use different themes on different pages, by using “custom templates” and just have the custom pages call a different stylesheet.

So you mean manually hardcode/define the theme to be used on page in the template.php?

Would this work with child themes?

For instance, say the page that will have a different layout uses a stylesheet that is a child of a theme other than the one used for the rest of the site. Will that work?

I’d love to find a solution for this too. Anyone more knowledgeable than I have any ideas?

Might look at:
https://download.mikelopez.info/2006/10/17/wordpress-themed-categories-plugin/

But also review Template Hierarchy, Category Templates, Tag Templates, and Page Templates, for an understanding of how the template process allows you to control various aspects without changing to a different theme.