Is this her first trip to Europe?
Your itinerary may leave her with more memories of transportation than of experiences.
Is this an itinerary typical of your own travel experiences?
Choose to stay in one place in Barcelona for XX nights. Strive to do things a 14 year old girl will enjoy. Less on museums, more on activities, time at the beach and some shopping. Bargains can be found for inexpensive blouses which make for a great wearable memory and allow her to show off some of her trip to friends (better than photos). Allow time for window shopping. Stay up late at night, past midnight, and go Tapas hopping and be adventurous with tasting a variety of Tapas and provide a taste of Cava Sangria. Take a day trip to Montserrat, ez day trip via train. Parc Guell, Sagrada, Casa Battlo, Plaza Catalunya, El Cortes dept store, Palau de musica. We have done this with our daughter's at a similar age. Rent an apt for less money than a hotel and have more room to spread out and a kitchen.
Take the RENFE AVE to Madrid for XX nights. Take the time to visit one of the best museums in Europe, The Prado. Then walk up to Retiro Park where you can rent a boat for a joint row together. Take a day trip to Toledo.
Jump back on the AVE and head to Seville. AVE travel is excellent, buy second class tickets at a huge discount on line. Stay XX days in Seville. An excellent place for Flamenco.
From Seville fly to Paris where you can rent an apt. Stay the remainder of your trip and take some day trips. Visit a variety of districts and look for some additional bargains.
Have fun, focus on activities and create some wonderful memories. Less destinations provides more opportunities. Keep in mind the saying "Better to teach someone how to fish........" the same thought applies to travel.