Don't mean to be negative on the advice given on this website, but alot of the previous advice appears to be from people that either haven't travelled to the US and definetly haven't travelled with kids your age. I hope you are also getting advice from tripadvisor and such other sites and not solely relying on this one.
That being said, we have travelled numerous times with out kids, same ages as yours, and have done similar trips that you are planning. There is no way I would ever recommend cutting vegas in favour of DC. vegas has plenty of things for the kids to do, from shows like lion king, to magic shows, indoor circus etc etc. DC full of monuments and history, really not of interest to children.
I agree with the doing disneyworld rather than disneyland, since you are already going to be in the area, and even though you are going back home via LA, you can still do Hollywood if you wish and shopping before you leave, as anaheim is 45 - 1hr from Disneyland anyhow.
Kennedy Space Centre does sound good, but is around 45 mins at least from Orlando if you have a car, if you don't then costs a lot to catch a tour to take you all there, and would take virtually and entire day, which is better spent at disneyworld. there is nothing like disneyworld for kids, nothing, you can easily spend a week just there, and your kids are perfect age for this. You can never fit everything into one trip unless you go for 5 or 6 weeks.
Not sure if your dates are set but I would also really see if you have to go in July, it is summer vacation in the US and super busy particularly in orlando. I would suggest early Sept if at all possible or check dates in August where maybe major states begin to go back to school.