I think you're thinking about this a tad wrong. You don't necessarily need/want to "auto-click" on the category. Just redirect to the appropriate category on based on the date.
Just make use the the current day with PHP's date()
function, use wp_safe_redirect()
to redirect to the category using the day you just got, and wrap that all with is_front_page()
to make sure it's only fired if it's for the home page.
Now all requests to the home page will get redirected to the current days' category instead. Something like this should get you started:
add_action( 'template_redirect', 'load_category_by_day' );
function load_category_by_day(){
if( is_front_page() ){
$current_day = strtolower( date('l') ); // 'monday', 'sunday', etc.
wp_safe_redirect( site_url( "/category/$current_day/" ) );
}
}