Bring a few compact umbrellas. You'll need it for shade as you walk around/stand in line, esp for your 60 yr old parents. You'll feel and look like a dweeb but that will be better than passing out from heatstroke.
Get there early and do whatever rides your 4 yr old is tall enough for, 1st and see Shamu next (can't remember the layout...its been 4-5 yrs since I've been there). Then do whatever shows/attractions you want to do furthest from the entrance and then work your way towards the entrance. Believe me, at the end of a long hot day with crowds of people, you won't want to walk all the way from one end of the park to the gate at the end of the day.
This is how we survive Sea World.
The riverwalk isn't close by Sea World. You'll have to drive there. I suggest the Mission Trail if you want to the whole "Texas history" experience...do a self tour...your hotel should have a map of the trail.
Don't do any of the streetcar tours. They are a rip off.
Take a riverboat ride on the riverwalk. That is worth it.
San Ant has a great children's museum. Your 4 yr old will love it I promise!
If you are in the mood to walk a little, try visiting the lobbies of the Emily Morgan Hotel, Crockett Hotel and Menger Hotel. Old and antique-y but can offer a break from the heat and you can soak in some Texas history while you sit and cool off (or use the bathroom).
I also recommend walking around the convention center across the street from the rivercenter mall. The landscaping is really beautiful and connects to Hemisfair Park...it is nice walking grounds, shaded, has some misting stations to cool off, a waterfall park, and visit Towers of the Americas there where you can get a bird's eye view of the city (for some awesome pictures) and get alot of Texas history. The little film they offer about Texas is pretty neat too. My son was 5 when he first visited and he loved it.
Stop by Buckhorn Saloon...all things Texas...and wall to wall hunting mounts from deer to bear to zebra and everything in between.
gosh, I love San Ant. I could go on and on but I don't want to overwhelm you! have fun :)