If an employee is working at a facility in Idaho, they are told that there is a position for them with the company still, but they need to move to Oregon. Can they be denied unemployment if they do not want to move to Oregon since they have a home and a spouse who is also working in Idaho?
What about severance that is offered to others, if they turn down the position in another state, do they forfiet severance?

Whether they lose severance if they turn down an offer is entirely up to the company. The law does not address the issue. However, it would be rare for an employee who turned down available work to be granted severance. It's not impossible, and it will be up to the employer's policies. But it's rare.

Offhand I don't know if either ID or OR allows UI for "trailing spouses". Some states do. More states don't.