get_post_type_object() does not work with switch_to_blog()

When loading blog B (thankfully) it doesn’t load plugins which are active on blog A only, and switch_to_blog() (thankfully) doesn’t do that either.

You could trigger the update by using something like the JSON API (or XML-RPC, ewwww), or you could make sure the post type is registered both on blog A and blog B. Maybe set show_ui to false on blog B so it doesn’t clutter the user interface.