I don’t know Ile d Re but have been to La Rochelle a lot.
My recommendation for lunch would be either Andre - a large long established fish restaurant right on the port - bit touristy location but nice food, good for people watching and views, and very friendly relaxed service.
Or choose one of the restaurants on a little square off Rue de la Fourche. One is called Le Panier de Crabes and does seafood, but there are 3 or 4 others - a pizza place, a moules place, a bar/charcuterie place and one that does steak and fish of the day. All with outdoor tables in a pedestrian square under a huge tree. Really nice setting.
Definitely visit one of the two Ernest le Glacier branches for ice cream. Worth the queuing!
There is an excellent new playground right on the harbour with mist jets for cooling off on a hot day.
There is a small zoo in the Parc Charruyer if they like animals. The La Rochelle beach is just next door to there and is surprisingly nice (no shade). Also bungee trampolines and a few other fairground rides dotted about this area.
If the weather turns not great the Aquarium is excellent (but not cheap).
Park in Vieux Port Ouest car park to be closest to the ports (although if full you may need to diverge to Verdun car park).
Personally I wouldn’t try to do both in a day, the traffic across the bridge is heavy in summer so you could spend all day in the car.