I don’t do well with screens either! I am fine on roller coasters though.
What I would recommend is leaving the rides that are potentially problematic for later in the day so you can take a break if needed and not risk needing downtime during those critical morning hours.
But that said, there are plenty of gentler rides on the Disneyland side that you can retreat to in between more intense ones – basically everything in Fantasyland; MMRR in Toontown; Jungle Cruise and the treehouse in Adventureland; Haunted Mansion and Winnie the Pooh in New Orleans Square / Bayou; and Autopia and Buzz in Tomorrowland, etc.
Of course even those rides might be more than he can handle if he’s really not feeling well, in which case you could just find a seat in some air conditioning at a quick service restaurant.
Also this thread might be relevant – it is focused on WDW, but of course a lot of the rides at DL are the same.