Wracking my brains here and not coming up with much! There's the pier of course, nice and easy to trundle along but a complete rip-off nowadays. The Sealife Centre is always a hit with kids of all ages so would be great for bad weather. It does say disabled access on their website so it might be worth a quick phone call to ask how much of the aquarium you would actually be able to see. I think you can avoid all the steps down to the entrance by going under the subway that leads through to the beach.
Stanmer park as it's conker season? There are conker trees down near the road so you wouldn't have to go up into the woods and the tea-rooms in the village do yummy hot chocolate!
I don't know how far afield you want to travel but how about Paradise Park at Newhaven? Most of it is very easy to get around and the dinosaur trail is indoors.