Adding more days is great, but you would still need to cut if you don't want to go crazy and spend the whole time sniping at each other. Even if you add 10 days, here is what you are going to do:
Land in London May 23. Four nights, depart May 27--jet lagged afternoon, three days. Still tight for London.
Half day or more of travel to Paris, four nights, depart May 31--evening and three days. Still tight for Paris.
Half day or more to Frankfurt. Two nights, depart June 2--evening and a day. Maybe at this point you can do laundry?
Half day to Munich. Three nights, depart June 5--afternoon and two days. No side trips to Dachau or Füssen.
Half day to Zürich. Two nights, depart June 7--afternoon and one day. See the Swiss Alps from a distance.
Half day to Milan. Two nights, depart June 9--afternoon and one day. You still haven't had time to just sit in a cafe.
Half day to Rome. Three nights, depart June 13--afternoon and two days. All this rushing and people are getting snippy.
Full day to Barcelona. Three nights, depart June 16--two full days. Another city, another two days of rushing around seeing the sights.
Half day to Cordoba. Two nights, depart June 18. You have accomplished your trip, but you are worn out, feel like you missed a whole lot in every city and will have to revisit, and spent a total of five days of your itinerary just traveling from place to place.
Next year, you book the same trip, hitting the things you missed in each place. Both years you spend tons of money and time and energy on transport.
Again, train is great for an easier way to travel--but you are still beholden to schedules. You are hauling luggage from hotel to station, eating station food (fine here and there, but you could instead be enjoying local cuisine), sitting still and watching the world rush by, hauling luggage from station to hotel, spending time checking in, etc. Now add in the inevitable time at each hotel spent settling into the room, changing clothes, and going to the bathroom and you lost still more time in each place--and your shoulders are sore.
Each city will have a crazy tight itinerary--we have to be at X place by this time so we can still get tickets to this museum, where we have exactly one hour. We have pre-booked this site at this time. I know we just spotted this cool eatery, but we have to pass or we won't have time to see the Eiffel Tower during our stay. We still haven't recovered from our jetlag this long in because we have been on the GO GO GO.
Have you been abroad before? Every one of your senses will be overloaded--European cars feel and smell different.
The sounds are different. You might not be able to read the language. Your brain will be exhausted even in a place like London, which is easy and where the language is the same. When you are trying to figure out the basics like public transport or remembering which way to look when crossing the street, that takes mental energy, even if it isn't hard. Walking on concrete or cobbles for extended times is exhausting. Museums require brain breaks.
I have done fairly ambitious itineraries, but with a full tour. Zero logistics, bus and guide, prepurchased tickets, door to door hotel, luggage assistance, a guide who can troubleshoot, a guide who can tell you what you are seeing so you neither miss things nor have to spend time / energy researching. And these are great, but still exhausting after 10 days.
I still think you should cut. Even with added days I would cut Frankfurt, Milan, and Cordoba, maybe even Zurich.
OR
I would cut by country / region and save those for the next trip.