The Chinese citizens are in their 70s, and may not speak English. Why would you subject them to getting an unnecessary visa that requires a day trip to be fingerprinted plus documentation of their recent life history, just to take an extra flight which also involves an LHR terminal change and passing through an extra security screening in both directions?
Fly direct to Madrid (flights arrive in the evening), get straight to a hotel and relax/adjust timezone, then take a train to Barcelona in the morning. OK, the high speed trains in Spain have security screening but it is nothing like in an airport.
Yeah, they freaked at the idea of getting another visa, we're flying direct to Madrid. One of them is well enough traveled that I'm surprised at her reaction.