I would never leave Jackson behind if I were moving but him and I are literally two peas in a pod.
We are always together lol. He's 100% my dog. He's used to traveling and doing new things so I think he'd adjust well, as long as we are together, he doesn't seem to have a problem.
I am sure he would miss everyone we are living with (my mom, stepdad and sister) but the dog will have to adjust either way. Leaving him at home will just cause him to create a stronger bond with your parents, IMO, and make it even harder to take him in the future. Might as well do it now.
I sleep at my dads house a few nights a week as well and they have two dogs - Jackson always gets a bit sad when we leave but then he's happy to be back in our regular home too. They adjust.