Why can't you place besuchen after uns? Is there a specific rule that I am missing? Or is it just a feel thing?
A simple statement has the conjugated verb in the second position.
Here, besuchen is the verb form that is conjugated for the subject meine Eltern: the -en ending is third person plural.
Thus it is in second position in the sentence, immediately after the subject meine Eltern.
Meine? Not mein??
Not mein. Die Eltern...
No. Eltern is plural, so you need meine before that word.