Suggestions for Notifications at each location

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Looking for some suggestions for the best setup for the following:

I have multiple brick and mortar locations, each has it own inventory and it reflects in a single Shopify website.  Each store gets orders from the website based on in-stock items.  Currently we have a centralized notification when an order comes in, then that central person tells the correct store to pull the needed items and ship.  I am looking for a better notification process flow.  I would still like a central notification as i get now, but i would also like a store based notification on the register (ipads), but ONLY for the store that had the items for the order. .. I have installed a push-notification system prior for the ipads/registers but I couldn't figure out a way to only have the notification go to one particular store and not another.

My current setup is this: Order comes in it goes to a central person who handles all orders, We also have a special email setup for orders that triggers a Push Notification to an app on the ipad/registers. Person working on the floor of the store is alerted by the push notification and pulls the items ASAP waiting for the central person to take it from there.  However the problem is there is no way to split the push notification per-store where the order is being pulled from.    This setup sometimes confuses employees as to which store is supposed to pull it

Any suggestions for process flow would be helpful