How do I target the child theme with get_bloginfo();?

Question

Try get_stylesheet_directory_uri(); which

Retrieves stylesheet directory URI for the current theme/child theme

/* ==  Custom Login Logo ==============================*/
function custom_login_logo() {
    echo '<style>
        .login h1 a { background:url('.get_stylesheet_directory_uri().'/images/logo-white.png) 0 0;background-size:218px 32px;height:32px;margin-bottom:10px;margin-left:20px;padding:0;width:218px }
    </style>';
}
add_action('login_head', 'custom_login_logo');

You might need to modify the path to your image slightly depending on it’s place in your theme’s folder structure