Hey. Have you checked out some multi-store syncing apps already available on the Shopify App Store? For example, Syncio: https://apps.shopify.com/syncio seems to be a good one which does exactly why you want - syncing inventory numbers between the 2 stores.
As for your second requirement on managing negative inventory, I’m not too sure about that one.
If you don’t find what you are looking for, send us a message and we are happy to see what we can do for you! Check us out at shypyard.io. We are a Shopify Expert certified agency that specializes in creating customized integrations and automations for Shopify merchants. This definitely sounds like something we are interested in working with you on! 
Feel free to book a free consultation and we’d be happy to chat.
Cheers!
Courtney