OP have you been on these campuses? The UCLA campus is huge and hilly. I’ve never been on the Duke campus so I can’t compare that one. You may want to post your question in each school’s forum, but the most reliable way is to call each school’s disability office.
I can understand your parents’ desire to be protective and to be available if you need help. But it also sounds like they want to tag along for the ride and enjoy the experience with you. There are schools (usually large publics) that are have a significant number of commuters and students living off campus. That’s definitely not Pomona though. The residential life experience is considered to be one of the great attractions of liberal arts colleges.
Have your parents thought through where you and they are going to live, and where to park if they are taking you to campus? Have they looked into the availability and cost of off campus housing for a family? I think the ideal situation would be to live on campus at Pomona but have your parents living in one of the neighboring suburbs. But they should let you have as much independence as possible.