Best ways to travel from Barcelona to Granada and Seville

Fly to Granada. Take the bus to Seville and then take the train to.Madrid.
You may be trying to do too much too short of time

Unfortunately, 6 nights is not even close to enough time to see Barcelona, Sevilla, Granada, and Madrid. You will have barely enough time to see two cities, let alone four very site-rich ones. Not knowing your interests, I would strongly recommend you consider only Barcelona (4 nights) and Madrid (2 nights) and use the AVE high speed train to travel between the two.

A variation on Carlos's suggestion would be Barcelona for 4 nights and 2 nights in Toledo. Toledo is about 30 minutes from Madrid. I think Toledo is culturally and historically more interesting than Madrid. A trip to Barcelona and Toledo would at least give you a taste of two different areas/regions--Catalunya and Castille/La Mancha.

What if we just did Barcelona, Granada and Seville?
We don’t have our flight back yet.
Would anyone suggest going North to San Sebastián and that area instead with the limited time we have.

I would not try to do 3 cities when you have only 6 full days. Barcelona alone could actually fill all your time. It's a shame to spend a lot of time on trains or buses when you have only 6 days to begin with.

Unfortunately, the Basque Country isn't any easier to reach than Seville. San Sebastian is 5 hr. 40 min. to 7 hr. by train; Seville is 5 hr. 30 min. to 6 hr. Including either of those cities turns your 6-day trip into approximately a 4-1/2 day trip.

For a more efficient trip (more sightseeing, less time staring out the windows of trains or buses) I recommend Barcelona with a side-trip or two within Catalunya (Girona is lovely) or--if you can muster some interest in art museums, Barcelona + Madrid. You can get to Madrid in about 3 hours. Although I'm one of those who prefers Toledo (though I do like art), by the time you allow time to make a connection at Atocha Station in Madrid, it's going to take you at least 4 hours to get to Toledo.

My choice would definitely be to spend all my nights in Barcelona.

Well, maybe Barcelona and Sevilla?? Granada is just logistically harder. From Sevilla you can take a high speed train to Madrid for your flight home. You could fly between the two. Not to be nosy, but I see you are from Minnesota. Have you looked at airfare and itineraries? Flights to Spain from Minnesota have been pricey, so what you do may depend on whether Madrid or Barcelona is less expensive. When I flew to Barcelona, I had to connect thru Paris. When I flew to Madrid, I connected thru Atlanta, that of course makes your travel time longer. Any chance you could add some days? Just trying some ideas for you and your son. I spent some mom/sons time with my two sons in Europe. Good Memories, very special to get time alone with your kids.

"What if we just did Barcelona, Granada and Seville?"

Even that's pushing it, but if you don't mind a whirlwind, you can do it. That is, as long as you can get a flight into Barcelona, a flight from Barcelona to Granada (other options currently much slower), a bus or the bus/train combo from Granada to Seville, and a flight home from Seville.

Remember that you lose a half day, minimum, when you change cities. So, three cities means two changes, which loses time you don't really have.

"Would anyone suggest going North to San Sebastián and that area instead with the limited time we have"

Not in March. San Sebastián at that time of year is likely to be rainy, cool - and did I mention rainy? Its appeal is that in the summer, when much of Spain is an inferno, that region is nicely warm instead of baking. In March, much of the other parts of Spain will have nice weather - take advantage!

You have 7 nights. The day of arrival is usually a jet-lagged haze, and the day of departure is taken up with getting to the airport. So, you only have 6 usable sightseeing days. If your flight is already booked to arrive in Barcelona, one option is to spend all of your time in the Catalunya region. In addition to Barcelona, there's Montserrat, Figueres (Dali Museum), Girona, Tarragona, etc. Many of these can be seen easily as daytrips from Barcelona.

Barcelona itself not only has many sights, but many of them require timed tickets, so it can be difficult to work the logistics of a short visit (my sister had 5 nights and was very stressed trying to get all the reservations in order).

If you insist, you can see Barcelona and one other place. Madrid has the advantage of high speed trains taking under 3 hours from Barcelona, so it's quick and low hassle. To get to Granada from Barcelona, you'd need a flight or a long train ride taking much of the day. You need at least one night in Granada to make the logistics work for a visit to the Alhambra. And don't go to Granada if you can't get Alhambra tickets in advance (they sell out every day in advance - check NOW if interested).

Sorry if I'm being a downer, but we want you to see Spain, not just Spain's train stations, bus stations, and airports!

Always buy tickets from the official website:
Sagrada Familia: https://tickets.sagradafamilia.org/site/SagradaFamilia/?lang=en
Park Guell: http://www.parkguell.cat/en/buy-tickets/
Alhambra: https://tickets.alhambra-patronato.es/en/tickets-alhambra-general/
Seville Cathedral: http://articketing.vocces.com/

I think Barcelona, Granada and Seville would be a great trip! Full disclosure - we didn't make it to Granada, opting for more time in Madrid, Barcelona and Seville. The best sites to purchase tickets (IMHO) are always the sites of the particular venue.

My standard suggestion for Barcelona is to take the 10-15 minute from Sagrada Familia to the Saint Pau Modernista site. No advance reservations required - and you won't be sorry. The other suggestion is to visit Sagrada Familia and Park Guell on different days if at all possible.

We used this company for 3 small-group day trips out of Barcelona, and highly recommend them:

https://spanish-trails.com/tours/

Thank you all for your very helpful comments
Looks like we are being too ambitious.
I’ll be flying from Minneapolis on the 4th to meet my son in Seattle .
We will then fly from Seattle on the 5th arriving on the 6 th to Barcelona.
Maybe we can try and fly to Granada from Barcelona then either fly back to Barcelona to come back home or fly to Madrid and fly home from there on the 13 th.