Our platform specialises in connecting up multiple stores and managing everything either from our product data management system or you can set one store to act as a primary and update inventory from there. The way we structure the data flows is that you can specify which products you actually feed to your secondary stores rather than everything.
Another thing to consider is to accurately track stock levels you will need to be capturing all orders from both stores. You could push all orders into one store and that would then adjust your inventory levels or we can capture everything into our system and recalculate stock levels accordingly.
Let me know if you would like to discuss further or test out our system. You can contact me at firstname.lastname@example.org
Channelup is a product data management solution helping Shopify stores automate their processes. If you require custom development or would like to test out our features contact me at email@example.com