9 nights in Spain Flying in and out of Madrid. Add Barcelona or Andalucia?

What would help us help you decide? Both are perfectly reasonable choices for four days. We'll all have preferences, other than size, I cannot think of something that would be a factor--it really comes down to personal interest!
I would only suggest you consider doing your side trip first so you can put all of your Madrid time together (versus having to come back for the night before the flight home if you book round trip MAD).

A third option would be to stay in Madrid for the entire time and take a few day-trips. Toledo, Segovia, Burgos, Avila, etc. are easy (by railway) and all worth visiting.

Between Barcelona and Sevilla, there is more of interest in Sevilla. But both are worthwhile, so I might flip a coin.

I’m planning a similar trip, 9 nights in Spain, for March 2026. I’m going to see Madrid and Seville. I am saving Barcelona and northern Spain for a separate trip.

I plan to split my time in Madrid—2 nights Madrid, 5 nights Seville, 2 nights Madrid.

Nick made a great point, as there are so many day trips one can do from Madrid.
It would not be so terrible to split the stay, after all, as you could have dinner with daughter and tell her about your travels, so I would not bend over backward to make it happen if you understandably want to spend time with her before setting off.

Having just visited all 3 cities this past April, I feel that you don't need 4 days in Sevilla. 2-3 days in Sevilla is plenty; but it also depends on what you like to do and experience and at what pace you like to do so. In 2 days in Sevilla we saw the Alcazar, Catedral, Plaza de Espana and attended a flamenco show. If it were me, I would spend the 4 days in Barcelona as there is a lot to see and do , more than in Sevilla.

Great input from everyone! I should also mention we’ll be there the end of March/early April this year.

In this case, month won't have much of an effect. I would flip through your guidebook (or on a website) and see what captivates you.

If you choose Sevilla, you could add Cordoba as a day trip from there. You could also do a day trip from Madrid to the lovely Toledo. If so, maybe five nights in Madrid and four in Seville. Or, if you go to Barcelona, you could take day trips to Girona and Montserrat. The high-speed train from Madrid is 2.5 hours to Seville as is , I believe, the train from Madrid to Barcelona, so apples to apples.
Either way, you can't go wrong. Spain is one of my favorite countries.

Between Barcelona and Seville, I would recommend Seville.
Also, do NOT miss Toledo and Segovia near Madrid.

At that time of year, the orange trees might be in bloom in Sevilla. If that’s the case, I vote Sevilla!