CAn you see all the shows in one day?
I'd say maybe, depending on the hours that the park is open, and the ages and size of your group. There are 5 shows at SeaWorld (Shamu, Pets Ahoy, Odyssea, Clyde and Seamore, and Dolphin Show). Odyssea is not an animal show, more like a Cirque de Soleil type show. Currently, the Dolphin Show is closed for rehab.
If you visit in the off-season when the park is open until only 6 or 7, then you may be able to see all of the shows, but you may not be able ride all of the rides, or see all of the other attractions (Wild Arctic, Manatees, Penguins etc.). And depending on the show schedule, it can be difficult to get from one show to the next. You may have to go across the park to get to a show in 5 minutes.
If you have the time, I'd take advantage of the second day free (within 7 days of your first park visit) that you can get at the window when leaving the park. It would give you a lot more time to enjoy the exhibits, rides and shows without rushing from one to the next.
This is just from my experience when we last went in May with a 5 year old and 2 year old. We spent probably an hour in the Penguin exhibit, 30 minutes at the touch pool, fed the dolphins, an hour in Wild Arctic, and didn't see Clyde & Seamore, Pets Ahoy or Odyssea, and didn't do any rides on our first day and we were at the park from opening until closing (7:00 p.m.) Granted our kids love sea creatures, so we took our time and didn't rush anything. So, we needed two days to see all of the shows and everything we wanted.