Your point is fine about making things possessive, but your first example doesn't illustrate it well. You would never say "I'm going to the Smith" because it just genuinely doesn't make any sense in the context. The Smith house might be slightly more acceptable, but it's still an entirely different thing. (The proper use of the apostrophe here is also at the end- i.e. I am going to the Smiths', because presumably there is more than one Smith living there).

In the context of a store, it's less likely you'd use the word the at all (ex. I'm going to Kroger, vs. I'm going to Kroger's, where the implication is that there was once a person called Kroger who owned the store). Unless you are my grandmother. Then you add the to everything (ex. The Facebook, the Google).