Okay, I am just chiming in here because for me an itinerary is created specifically so I can do something and see something that is high on my list! Saying that you want to "sightsee" is a very vague way of describing your personal interests.
Your trip sounds like you just kind of picked three cities that had a certain appeal, and put them on the check-off list, sorry.
A few nights in a major city like Paris without seeing anything else of France is just a brief introduction (and will be quite busy).
Three nights in Amsterdam when time will be spent with friends means three nights probably NOT being a tourist.
Finally, I love Spain like a second home, but Barcelona would never be my first choice of a city to visit without seeing any others.
I do not think that this is a go-go-go trip, although anybody a can make a trip become like that, because you have not listed anything at all really that you plan to do. For instance, on my first trip to Paris with five days I did a day trip to Rouen and Giverny, a day trip to Fontainebleau, a tour of Versailles, visits to the Louvre, Notre Dame (up to the roof), the Eiffel Tower (climbed to the top) Sacré Coeur (my father's favorite stained glass window), Cluny museum (I have copies of the tapestries in my home), Gustave Moreau museum (a personal favorite), bateaux mouche cruise dinner, and of course, shopping and hotel touring (I like to pop in to some of my favorites). There are oodles more things to do in this fabulous city. (We then rented a car and drove around France for another two and a half weeks.)
How fit is your mother? Can she walk a lot? Does she have good endurance? Do you recover well from jet lag? Do you and she both do okay in hot weather? What are her interests and goals for this trip?
I often travel to Europe in Summer, and I am well aware before I leave what may be closed, and I have never had any issues with my list of must-do's. I happen to prioritize castles and cathedrals when I travel in Europe, so they are always first to visit. Sometimes I even reserve my restaurants for both lunch and dinner in advance!
Well, you can certainly go to Monserrat when you are in Barcelona, and flights to Mallorca are cheap and only about an hour one way, but why choose Mallorca over Madrid? Mallorca is quite charming, but both Mallorca and Barcelona have been heavily inundated with tourists these past few years, and pickpockets abound. Be aware you also need to secure advance reservations for many of the sights in Barcelona.
One thing I always tell people planning trips is to look at a good travel and tour book to see what they highlight for tourists to see and do. Since you are on the Rick Steves website you can certainly review many of his recommendations.
I think you have the outline of a potential trip, but you need to figure out if it will provide true satisfaction of visiting each place. For me, I try to spend at least a week or two in just one country, so I get to know the country a little and understand some of its culture. I do understand the distance you are traveling, however, so I would say decide what you want to see and do the most, and try to reorganize your days based on that.
Have fun planning!
