Have two different URLs show the homepage

WordPress will always try to redirect to the canonical URL to prevent duplicate content, so you’ll have to disable that mechanism to get another URL to display that page.

First, your rewrite rule:

add_rewrite_rule('^page1', 'index.php?pagename=your-page-name', 'top');

Then filter redirect_canonical to return false if the requested URL is your 2nd home URL:

function my_redir_check( $redirect_url, $requested_url ){
    if( home_url( '/page1/' ) == trailingslashit( $requested_url ) ){
        return false;
    }
    return $redirect_url;
}
add_filter( 'redirect_canonical', 'my_redir_check', 10, 2 );