Different approaches might be applicable - depending on the scenario you are facing - for example, your assumption that the sales patterns are highly correlated needs to be tested. For example: my choice of cars might not be between the 2 models you are referring to - but between similar models from different vendors.
A time series modeling based approach might be to consider modeling the sales amounts of cars (P1 and P2) in an hierarchical fashion - which means that you would aggregate the total sales and model all 3 series independently. Then you could adjust the individual forecasts by the total forecasting using a top-down reconciliation approach.
If your two product types encompass most of the market then it might be a good idea to model Total car sales (product1+product2) and Car type preference (product1-product2) separately instead of each product type, as a function of your predictors (X1, X2, ...)
Mind you, with a single year's data, you will miss any effect that affects all cities at the same time, such as gas prices, interest rates or consumer optimism.
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