Hi,
This is exactly what our app does, please check it out here https://apps.shopify.com/syncerize
Your dropshipper will connect with your store using our app, he can import your products to his store and even add %margins automatically or can set his own price.
Whenever an order is placed, it will automatically be pushed to you for fulfilment
and when you ship the order to his customer, his order status and his customer will be updated.
Let me know if you need help in setting it up