Looks to me like a single company will be the simplest and most robust solution. You will need two warehouses (one per shop) You will need two shops. Since you are a single company both shops will automatically share products and customers. Note that average cost is at a company level - not sure if this is an issue.

Issues: 1. security - I would create different user groups for the shop object - shop 1 and shop 2 etc and put a record rule in that limits what records they can see. Will need to do the same for warehouse if they are using SO (don't think they can change warehouse for POS?).
2. need to think about the journals. you could use an analytic account on the shop to be able to differentiate the revenue when posted, but you probably want to have separate sales and cost of sales accounts? Depends if you are running anglo-saxon accounting or not. This area may require some development depending on what you want.

I think you are largely on the right track