How to maintain wp_enqueue_style dependencies set in parent theme style enqueuing

I’m sure you missed it but the dependency parameter should be an array and not a string.

So your enqueue function should be:

function child_enqueue_styles() {
    wp_enqueue_style( 'parent-style', get_template_directory_uri() . '/style.css', array('bootstrap'));
}

or:

function child_enqueue_styles() {
    wp_enqueue_style( 'parent-bootstrap', get_template_directory_uri().'/css/bootstrap.min.css');
    wp_enqueue_style( 'parent-style', get_template_directory_uri() . '/style.css', array('parent-bootstrap'));
}

Reference: wp_enqueue_style