We just returned from a 2-week vacation in Spain with my 2 kids, ages 13 and 12. We only spent an afternoon in Madrid (my personal preference based on previous trips; to each his own).
With respect to kids in art museums, I had my daughter pick a painting that might interest her (she chose "Guernica"). At home, prior to the trip, she spent time researching the painting: historical context, the painter's biography, history of the painting itself, etc. When we got to Madrid, she was excited to actually go to the Reina Sofia and see the painting itself; it was a lot more interesting than just a picture on a wall. After seeing "Guernica," we wandered through the museum looking at other art for about an hour, and then she was all done and we left in a good mood. So, we grownups got a taste of the art museum, and she didn't feel like we were torturing her. You could do the same for a piece or two at the Prado.
I would also encourage you to stay longer in Toledo. It is a wonderful place to "settle in" and feel like you are really in Spain. Consider traveling directly there from the airport and staying in Toledo and then doing a day trip to Madrid (depending on how much you want to see in Madrid). As the above poster said, it is easy to travel from Toledo to Sevilla, since you have to go through Atocha anyway. We did this on our trip (Toledo to Sevilla), and it was very efficient.
Also consider staying in an apartment vs. a hotel. Not sure how long your trip is, but we found that having the extra space in apartments was really nice; family closeness is great, but it's nice to have rooms to escape to for a little alone time on a longer trip! My kids especially liked retreating at the end of busy days for some quiet time in their rooms. And I found apartments to be really economical; our apartment in Toledo was an especially good bargain (and we loved it): https://www.casadelosmozarabes.com/
Make sure you don't miss San Gines in Madrid for churros and chocolate (just off of the Plaza Mayor)!