I'd probably look at setting up MSM (Multiple Site Manager). If you're not familiar, its an EE 1st Party addon that lets you have one install of EE on different URLs. So you could set it up so you had a sub-domain as the 'backend' cart system and then just secure it so only your client can get in if needs be. The front end would be as normal.
I would also suggest looking into Cartthrob for this - The support is a bit pants at the moment with CT, but you have so much more flexibility. I love store, but I set up three shops in the manner for a client not so long ago, I went down the route of Store and hit a few brick walls.
CT takes longer to set up as you have an insane amount of control over what is happening. For example I set up the three stores using MSM and then had one category section for each site. This way the client can control what products are in what category and therefore what site they show on. Not only that, but you could also have different prices if you so wished. I believe this isn't possible with Store at the moment, but I could be wrong.
Overall, you could do it with Store and I'd just look into MSM from EllisLab. However, for this project, I'd strongly advise you take a good look at CT - Although it is a lot more expensive, there is more control for those - 'Can we do this' moments the client will no doubt throw at you in the future.