Candace, we do that with Stitch Labs:
http://apps.shopify.com/stitch-labs
You can choose which store is master - we use Stitch as the master. Our primary goal was the same as yours - "share" inventory between the two Shopify channels. What's great is that you also great reporting that can be aggregate across your channels or just one. Once we dove in, we ended up listing again on Amazon because we no longer had the manual headache of making sure we had stock for what we were listing. Stitch sends that out to Amazon too.
Nice design, excellent support. You might want to give it a look.