I went to the school when my principal arrived at my home.
Does it mean I was in school when when principal came to my home?
I interpret it to mean that when the principal arrived, you left home to go to school. If you wanted to say you were already at school when the principal came to your home you'd say
I was [already] at school when the principal came to my home.
As for your other example,
We went to water park this summer.
You should use an article with "water park": Either "a water park" or "the water park". Use a if person talking to you doesn't know, and it isn't important, which water park you went to. Use the if the person you're talking to would know exactly which water park you are referring to, or if there's only one water park that it would make sense for you to have gone to.
Use gone when you need the past participle form of to go, such as
I have gone to the water park many times.
I had gone to the water park in 2016 but in 2017 I never had time to go.