Recommendations for ~24 hour layover--is Toledo doable?

Segovia is too far. Toledo is possible, but very tight. If you decide to go for it, definitely buy your train tickets in advance, since you don't have much flexibility in times.

Your flight leaves for Dubrovnik at 10:30am? What time will you have to be at the airport?
Good luck!

If you rent a car, you could do either pretty easily. I'd travel straight to the Segovia/Toledo, spend four to six hours, then have lodging at least on the way toward the airport to save travel time in the morning. It's about 1 hour 15 minutes driving time to Toledo or 1 and 1/2 hours to Segovia from Barajas Airport. Remember to add time to get through immigration and pick up/drop off a car (and suitably early arrival).

You will likely get breakfast on the plain so lunch at your destination and dinner after you get checked into lodging makes sense. Your mother and 4 year old may not be used to eating times. Typically, dinner is later and tapas doesn't even start until 7 pm or later. If that's a problem, there are local cafeterias and recognizable American chains (KFC, Burger King, McDonald's, etc.) where you can get something to eat.

Don't forget to sleep on the plane or the day will be more of a death-march than fun experience.

Thank you for the replies. I want to try Toledo with a car, I think. It may save total time versus going to Atocha to get the AVE.

With a car I think Toledo is do-able; if you had to get on a 10:30 flight using AVE to Atocha and then express bus to Barajas, that would have to go perfectly at each step. Too risky.
For the evening in Toledo, there are both fun/gossipy and informative/historical correos nocturnos offered by several companies; all involve walking over uneven surfaces in the dark, though. Maybe better to see if there's a musical performance at one of the churches.
For a Castilian dinner, consider restaurante El Cobertizo -- internal tourists, probably, but English/Americans, probably not.
For new cuisine, I have a place but don't want to post it to the general board.

Doable by car. An overnight is not possible by train, IMO. Figure an hour to get out of the airport, 45 minutes on the express shuttle to Atocha, that means an afternoon train to Toledo, then you really need to go back to Madrid that night for your flight (10:30 plane means arrive at airport at 9, and I don't think there are any trains that early). You'd need to get to Atocha by 8 then the bus. Way too tight. So you could take a 8PM train back to Madrid, leaving you with a few hours in Toledo. Technically possible, if you REALLY want to see Toledo.

By car is an option with more time in Toledo. But I'd stay in Madrid and enjoy it. Here's why:

If your plane is coming from the US/Canada (i.e. you're not visiting somewhere else in europe first then taking a short flight to Madrid), I'd think carefully about jet lag. If you travel enough to know you won't be horribly affected, great. Many people (not all) are extremely tired on landing day - it's a different kind of tired. On my first trip to Madrid, I landed at 9AM and had a train to Seville at 7PM. I figured I'd see the top sites in the city in that day and head on. I did, but it was kind of miserable and my memory is lacking. Add a 4 year old and I'd imagine it's worse. My kids are total disasters on landing day. It's just a given in our family. Hard enough for me. My version of jet lag is an awful arrival day, bed at normal time, and perfectly fine from then on. Everyone is different. I'd be hesitant to drive in a foreign country on arrival day after an international flight. But this varies and if you don't experience jet lag this way, great!

Stay in Madrid. Enjoy Retiro Park (nice, relaxing, there's a playground). Do a museum (pick one!). Sit and have a long lunch with wine and jamon. Go to the food market. Go to the Palace. Get a hotel, go to sleep by 9 (obscenely early for Spain, but you'll need your energy for the rest of your trip!)

Good point about landing day being rough. I am usually totally fine but my dear husband can be a wreck.

I once landed in Paris CDG in the morning from the US and rented a car to drive east to Giverny and beyond. I got stuck in Paris morning rush hour. It was awful. Another time I landed in Shannon, Ireland at 6 AM (1 AM US time) and got to drive on the opposite side of the road. That was nuts too.

Thanks for everyone's feedback! Jury is still out on what I will decide, but the feedback on the car if I do go is very useful.

I agree that an overnight in Toledo would be too risky with a 1030am flight to Croatia.
That is if you are relying on trains. With a rental car it would be feasible with an early start.
My advice would be to get back to Madrid in the evening to be near the airport.
This however cuts into your time, perhaps not making it worthwhile.
With 4 of you, a 24 hour car rental from Barajas may be a cost effective option anyhow.
I would want to leave Toledo by 6am the following day though, allowing for traffic and returning the car.

It may be a gamble, but I opted to rent a car for the day and try it. We will have the afternoon and evening in Toledo, which is better than nothing! If anyone is a zombie they can do a quick power nap and have the evening at least.

I'll plan to leave EARLY to make it back in time for our 10:30 flight to Dubrovnik.

I'll give a trip report once we are done and let everyone know how it went.

Having just done a day trip to Toledo from Madrid, what you want to do is really unrealistic and--to me, anyway--very stressful. We easily went to Toledo by train in the morning and early evening and had more time than we needed. But you have to factor in the time it would take to get to a train station and/or car rental and how you're going to get back to the Madrid airport by 8:30 in the morning.

And what if your plane doesn't land on time?

If it was just you and your husband I guess it would be OK to risk such an endeavor but not with a 71 and a 4 year old in the group.

Madrid is a wonderful city; just spend the day there.

I think you will be fine with a rental car - not so by train as you say.
Hopefully you could be in Toledo by 2pm, all going well.
I would make sure I am on the road by 7am next morning for a 10.30am flight.
Enjoy.