It ended up being something very easy, but something I overlooked. Since I always use <?php get_search_form(); ?> for my search forms, I naturally assume that in my section template for the search area, I was using that, but I was not.
I built the theme custom off of another theme I built for a different website and for some reason in the form’s action="" I hardcode the url for the first site; that is why I kept getting forwarded there.
I thought I checked the section, but must have overlooked it. After two days or so, I decided to re-check the section, thanks to the suggestions in the comments which made me re-think the problem.
So yeah, really stupid brain fart, but it is now solved.