As part of a larger trip, we will be in Spain for a week. So far, we have only been to Barcelona and Malaga. Starting in Barcelona (where plan to spend 2-3 days there this time), and the Prada in Madrid is a must, what would be a recommended itinerary using public transport (preferably trains) only. We need to end in northern Portugal at the end of that week.

Check RENFE , Spanish railway network for connections..
Barcelona - Madrid is an easy trip by fast train , 2:30 - 3:00 hours.

Since you have only one week, and may spend up to three days in Barcelona, I think you have essentially proposed the itinerary you seek -- I'm not sure how much more you can cram into a week, besides two great cities like Barcelona and Madrid, without being too rushed. Since you have been to Spain, you are probably already aware of easy one- or two-night trips you night take from either of those cities, like Girona in Catalonia, or Toledo near Madrid.
Though it doesn't get much attention on this forum, Zaragoza may be worth considering. It's a convenient stop on the train route between Barcelona and Madrid, and if I might assume that it has changed little since my 2009 visit, it's well worth at least a night, though two nights would be my recommended minimum. (I think I spent four there.) In addition to ancient Roman ruins and a well-preserved medieval palace (originally Moorish), and a quaint historic center, there were, at least at the time of my visit, two or three Goya museums, which your interest in the Prado inspired me to mention.

I visited Zaragoza a few years ago on a day trip from Madrid.
A very nice spot , I wished I had time to stay at least overnight.
Both, the famous Basilica and the Cathedral are worth the visit
to the city. .