you can create this structure as follows

Multiple Home pages

1 Catalogue

Your purposed structure is like below

Home1

• Shop (Starting node)
  • Product 1
• Home2
  • Shop2 (starting node)
    • Product

If you create a property in Site Settings that just take Starting node against each home page

Product-1 can be in multiple categories (Shop & Shop2)

Now in the Commerce Initialization module, you can define how your commerce Urls rendered. You can specify like

{Home page}/{Starting Node}/

All products in starting nodes and sub-nodes will work and use your Product controller. 

forgot to add a code snippet 

    [InitializableModule]
    [ModuleDependency(typeof(EPiServer.Commerce.Initialization.InitializationModule))]
    public class InitializationModule : IInitializableModule
    {
        public void Initialize(InitializationEngine context)
        {

            var referenceConverter = context.Locate.Advanced.GetInstance<Mediachase.Commerce.Catalog.ReferenceConverter>();
            var contentLoader = context.Locate.Advanced.GetInstance<IContentLoader>();

            var catalogs = contentLoader.GetChildren<CatalogContentBase>(referenceConverter.GetRootLink()).ToList();
            if (!catalogs.Any()) return;

            var siteDefinitionRepository = context.Locate.Advanced.GetInstance<ISiteDefinitionRepository>();
            var siteDefinitions = siteDefinitionRepository.List();
            foreach (var siteDefinition in siteDefinitions)
            {
// Get your node from catalogue based on site defination
                var catalogPartialRouter = new HierarchicalCatalogPartialRouter(() => siteDefinition.StartPage, your-desired-node, false);
                RouteTable.Routes.RegisterPartialRouter(catalogPartialRouter);
            }
        }
     public void Preload(string[] parameters) { }

        public void Uninitialize(InitializationEngine context)
        {
     
      }
    }