Definitely do both. Being in Hutton allows you to take honors classes if you want to, but you are not required to take any. It basically just opens up more options for scheduling. Hutton does offer an honors notation if you take enough honors classes, but you don’t have to get the notation.
There are literally no drawbacks to being in Hutton because you don’t have to take any honors class you don’t want to. Kelley offers honors versions of some classes that you can only take if you are in Hutton, and Hutton also offers its own gen ed classes. It will make more sense during orientation, but just accept the Hutton invitation.