Shopify is beyond amazing. I love it so much. Best eCommerce solution hands down. No script or plugin in the world can even come close. Great choice.
The solution would simply be to make two sites that look exactly alike and have them link back and forth to each other… as you are suggesting. There’s no way to have them “live” together though as they are two completely different beasts. Plus Shopify is hosted (no FTP access). Not ideal really since your logins won’t be integrated. Not sure if there’s a solution to that.