I have a problem with displaying children pages of custom post type

EDIT
So if i understand correctly what you want is

$children = get_posts( array( 'parent'=> get_the_ID() )); // 'post_type' => 'all_products' in option

Have you tried removing “parent”=>0, meaning that a page has no parent like this

$children = get_pages( array( 'child_of' => $post->ID, 'post_type' => 'svi_proizvodi' ));

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