We went in March. The regular bus tour that was part of general admission (I think about $30 pp) was excellent // opportunity to see launch sites in the distance and then a stop at the Vehicle Assembly plants (excellent little movie about the history of the space program / background on cold war) // opportunity to see old control room - so much improved over the tour 10 years ago -- I was impressed.
I would make doing the tour your number 1 priority. We only got there at 1 p.m. so just did the tour (maybe 2 1/2 hours as we looked around in gift shops, etc. too), the shuttle launch experience, and visited the rocket garden (very enjoyable 1/2 day) // something else that looked really cool, but we couldn't do due to timing was go to one of the talks with an astronaut. IMAX movies are included too if you would like to see one of these. We had already seen the one at our local science center, and didn't have time to fit in the other we hadn't seen.
I think it would be easy to do a full day there, but even with a 1/2 day we felt it was well worth going and that worked great for us.
Maybe someone else with younger children can answer if they think your kids would enjoy this. Ages in our party were age 15+ and I'm more in tune to what teens enjoy vs. younger children. (I don't know if they would love it, be bored, etc.) My guess is if they enjoy a day at a regular Science Center they would probably like this too (not as much as the Magic Kingdom or Sea World, but I'm guessing it would be a fun day or 1/2 day for you.)