A question to those who know Madrid well... Is there a commuter suburb that you would recommend for visitors with cars, who do not want to take the car into the city centre? It's fine if it's soulless and lacks charm. The main requirement is that it have easy access to the city, on one of the cercanía lines. (Do these typically have some form of park and ride lots?)
How long will you be in Madrid? You could return the car upon arrival and pick up another one to continue your trip. You really should stay in central Madrid.
Or park the car somewhere safe on the outskirts and take the cercania to the city with your luggage.
How about Toledo. It is a great place to visit and train and or bus is easy into Madrid.
I was hoping to spare you the long and complicated explanation, but the gist of it is this: I will be there for about 10 days, split evenly between Madrid and day trips. The kicker is I don't know which days I'll be day tripping, and I won't know until arrival (I'm meeting up with family there, and the other parties' schedule is extremely unpredictable.) Staying in central Madrid would work if we could day trip by train, but (1) according to RS, trains to popular destinations sell out and need to be purchased in advance, and I don't have the luxury of advance planning, as explained above (2) logistically, a car is easier/cheaper for 5 people, including children.
Toledo is a lovely idea, but I was hoping for something a bit closer. The ideal place would be akin to Haarlem (vs Amsterdam) or even Bromma (Stockholm).
Yes, trains to/from Toledo often sell out, but only a couple days in advance and only some trains. What day trips are you planning? Consider the amount of time you'll lose commuting into central Madrid, possibly on crowded trains. Also, if you stay in central Madrid, you can easily return to your room in the afternoon for a rest, or to change before going out in the evening. If you need to commute, you'll be out and about all day . . . with children.
I recommend the suburbs, but not too far. Traffic can be a little crazy. I can also recommend a good restaurant, La Posada de Vila. Wine selection is amazing.
Try a hotel that provides parking in the centre.
As the above comment says, try to find a hotel with onsite parking. I think this would be the best option.
Where do you plan to go on your day-trips?