Spain Vacation with Family

Spain is big. Either of your plans are better served with internal flights. Global warming has meant that by end May, Andalusia (Seville, Granada and environs can be pushing 100F)
With so few days, flying open jaw (in one city out the other) makes sense. In my opinion, neither option is ideal of adding a third city. Valencia is a 3ish hour bus ride, so the closest, but not worth the effort in my mind. As you don't state your interests, we can't really recommend options.

Depending on where you live, there may be flights from Seville or Granada that code share with an international flight that MAY make it feasible to have a 3rd city. Given that there are 8 of you, Seville may offer the most variety, but the Alhambra in Granada is world reknowned and for a short time would also work.
I would be inclined to spend more time in Madrid Toledo and Barcelona. Both Madrid and Barcelona offer options of day trips, and if anyone doesn't want to go that day, they can stay in the larger city.

I think the third city is not a good idea. Too much travel time for too little sightseeing time. You have allotted too little time to Barcelona, in my view, if you want to go inside some of the most popular sights. Many require pre-booked, timed tickets to avoid terribly long ticket lines and the possibility (likelihood?) of sell-outs before you reach the ticket booth. Even if you could teleport yourself, I would certainly choose a third full day in Barcelona over one day in Valencia or Malaga. Given that teleportation is not possible, I'd choose the extra day in Barcelona over either Seville or Granada.

Flying into Madrid and out of Barcelona, or vice versa, is a very good approach.

We travel often with our young children and our elderly parents and find it much easier not to be too ambitious. in our family at least, the kids need significant down time to enjoy themselves, and our parents just don't move that quickly, so we can't pack a lot into any given day.

Unless you think you'll never get a chance to go back to Spain for the rest of your life, you could consider just picking one base.

I might be in the minority here, but I think picking either Barcelona or Madrid for this trip might be better than trying to do both.

Not the question you asked, I fear, but with your limited time (and the need to herd eight people), I would split your time between Madrid and Barcelona and take a day-trip from each, or perhaps two from Madrid. If you can fly into one and out of the other, then all the better. Travel between the two is straightforward and quick by rail.

If you are determined to do three bases, then I think you need to drop Toledo, and go Madrid to Sevilla to Barcelona. I like Valencia very much, but I don't think it is a place for a first visit with limited time. Same comment for Malaga. Granada is Spain's second best city (Sevilla is the best), but public transport travel difficulties make it impractical for just a very short visit from the North.

Edit - there are some eight seat people carriers, so if you're able/willing to hire one of those, you could mix your itinerary more, but I still wouldn't plan something as widespread as either of your itineraries.

Day 9. Most flights for the US leave in the morning. You don't say where you are flying to/from. It's likely that you will need to be at the airport 3 hours prior to flight time. You need to allow close to an hour to get from the city center to the airport, whether it's Madrid or Barcelona. Unless you have a late afternoon or later flight, you should plan spend your last name in the city you are flying home from. Even if you have a late departure, consider whether you want to be hundreds of kilometers from the airport and chance something going wrong (a train strike is only one possibility) and 8 people missing a long-haul flight . . . .

Thank you all for your suggestions. I understand that the itinerary is difficult but we might not be able to do Spain again as we are travelling from India.

Like suggested we will fly in to Madrid and fly out of Barcelona.

The rough plan is like
Day 1 - Reach Madrid at night, check in the hotel and relax
Day2 - Sightseeing Madrid
Day 3- Day trip to Toledo and back to Madrid in evening - Take a tour plan
Day 4- Take a morning train from Madrid to Valencia
Day 5 -Spend the day in Valencia
Day 6- Travel from Valencia to Barcelona
Day 7 - Spend time in Barcelona
Day 8 - Barcelona
Day 9 - Fly out from Barcelona

We are planning to book hotels/stay in the city center for Madrid and Barcelona , so that my parents can stay back if they dont feel like walking.

Madrid has a few great free walking tours , and Barcelona does too. You can “tip” the guide whatever you think the tour was worth to you. Here are a few links:
https://strawberrytours.com/madrid
https://ogotours.com/landing/
https://runnerbeantours.com/
https://www.neweuropetours.eu/

Happy Travels✨💫

With 8 people going on this trip, I would keep to Madrid / Toledo and Barcelona. Spending two days of travel and one day in Valencia may well wear you and / or the rest of your travelers out. We are going to Spain in May, flying to Madrid, spending several days there with a long day in Toledo, then on to Barcelona fro several days before catching our cruise ship. We have been to Barcelona in the past, but will be concentrating on places that we have never visited. We have been to Valencia, nice place to visit if you had more time, not worth the time for a one day trip.

I have Valencia on my itinerary this year. It's my fourth trip to Spain. One of the earlier trips lasted 88 days, and this one will be at least 6 weeks. I'm sure I will enjoy Valencia, but it's way, way down on my list of places to go in Spain. Cutting Barcelona and Madrid/Toledo short in order to squeeze in Valencia--I don't understand that unless you just can't skip the Calatrava architecture. Including Valencia will substantially increase the time spent on trains (about 5 hours vs. as little as 2-1/2 hours--not to mention going back and forth to train stations four times instead of twice) and add a good bit of transportation expense.

You know, as much as Valencia is not a first tier city for Spain, it is different to Madrid and Barcelona and at least logical for transport. It has an old town and then a new area and a beach. Transport to Barcelona is easy and the bus is a comfortable pretty ride.
If this is what you have to work with, then take it and enjoy.