Child theme .css files are not overriding their parent .css files

Try running two seperate functions with an incremental priority..

function my_enqueue_style_one() {
wp_register_style( 'style1', get_template_directory_uri() . '/style1.css' );
wp_enqueue_style( 'style1' );
}
add_action( 'wp_enqueue_scripts', 'my_enqueue_style_one', 10 );

function my_enqueue_style_two() {
wp_register_style( 'style2', get_stylesheet_directory_uri() . '/style2.css' );
wp_enqueue_style( 'style2' );
}
add_action( 'wp_enqueue_scripts', 'my_enqueue_style_two', 20 );

also try registering the stylesheets prior to enqueuing them for additional control… like conditionally testing to see if they re already enqueued.

if ( ! wp_style_is( 'style1', 'enqueued') ) { ... }