Hello sir.
It does not really matter if you will choose the first or the second essay, because both are correct if you are the narrator
Both essays show you narrating and both show your father's truck. If you decide to choose the possessive adjective "our", you will just showing your brother in your essay, which won't make such a difference.
However, If you want to show later in your text that your father is not the same as your brother's father, then go with the first essay, so readers will understand later in your text that you have chose the possesseive adjective "my" instead of the "our" just to show that there were two different fathers and not the same father.
Please someone correct me if I'm doing some mistakes lol.