I am an intern at a marketing company, among other things, and my superiors tasked me with figuring out how to change specific products using an API. I need to figure out what section of the stores API is responsible for changing the available product count on the stores page. If 10 products are in the warehouse, 3 are marked as sold and are being prepared for shipping, and 7 are available we need to be able to adjust the available count in the store at the end of the day. Unfortunately, I do not have access to the clients store. I am unable to access the actual code for the API. If you can help me I would greatly appreciate it. I am willing to share as much as I can, per my NDA, to solve or come close to solving this issue.
If I understand the situation correctly your company is "drop shipping" to the consumer on your client's behalf. The ideal solution your are looking for will require API access to the client's store. The client's store will need a "location" that represents the inventory available from you as a supplier.
Note the text on that page: "Apps that stock inventory or fulfill orders for you are considered to be locations but don't count towards those limits. When you add such an app to your store, or when you first enable locations, the app is automatically added as a location."
I searched but did not find a published App that meets you needs, however it would be straight forward to create a custom app to integrate with your client's store that would make your available inventory visible to your client's store. I am assuming your system can provide this information.
We could also pull orders (or partial orders) for the products that need to be shipped from you as a supplier and send tracking information when you ship if your system supports those interfaces.