Show only TWO categories on home page

I am aware of many posts on this topic, and tried many of the solutions to those, but unfortunately I still was not able to resolve my problem.

On my homepage I wish to include all News and Agenda posts, and not the posts of other categories.
However, a plugin that excludes the other categories is of no use, since many newsitems also appear in another category (and that category should not be showed in total on the home page). (this is however how it is now on our homepage (www.nrin.nl), using RYO plugin for category visibility)
I do not have a home.php, nor front-page.php.
I tried to solve it by modifying ‘$query->is_home()’ in functions.php.
I already included something in index.php to adjust the order of the posts in all category pages (I wanted to sort it by title, not by date). However, on the homepage I do want the order to be by date (in reverse order).

Thank you very much for your suggestions. Please note that I’m a beginner ??