Well, I am not sure what the issue is about your "sanity."
Actually, I like your week-long itinerary--I think it is very doable and not overly stressful. I do not like to change hotels a lot when I travel--too hectic.
I am older than you and I have the energy and stamina to easily do this itinerary--or more!
Have you booked hotels yet? Hotels in convenient central locations will allow you to commute easily.
When you arrive in Madrid if you are not exhausted you can head over to the Plaza Mayor in the early evening and soak in the ambience, and try some tapas. Hopefully that will help you reset to the new time zone a bit.
You can easily see one museum as well as other sights the next day. Perhaps that evening you could go to a flamenco show in Madrid.
I love Toledo, and I would definitely not cancel your day trip, because it will provide you with a different perspective about the history and beauty of Spain.
Remember you will need advance tickets to many of the attractions in Barcelona. You will be strolling around Barcelona a lot the four nights that you stay there. The train from Madrid to Barcelona is fast and efficient--we just took it the opposite direction this past Summer as well. I booked with Iryo.
If you are willing to splurge and have someone take you on a formal walking tour, which is what I usually do when I have tight timelines, you can check out the tours offered by Take Walks. Last Summer I took the tour of the Prado and the Royal Palace with David, a superb guide. We also did the tapas and flamenco show with them, also fabulous. I highly recommend the company--I also use them in Italy. It is great to have the tickets paid for and ready, skip the lines, and have a very knowledgeable guide accompany you in a small group. We also took a bus tour to Toledo, but we included Segovia as well--very long and busy day, but an amazing tour going inside the Segovia Alcázar as well as the Toledo cathedral (both return visits for us.)
Please note I am completely bilingual in Spanish, I have lived, worked and gone to school in Spain and traveled there multiple times, but my husband is an English-only speaker, and we are busy with careers, home, and pets, so we can no longer travel for months as we used to--thus we try to make optimum use of our week or two-week vacations! Yes, one can always sleep on the plane on the way home.
Have a fantastic time--¡Buen viaje!
