1st trip to Spain and adding Paris.

You need a good guidebook and a sharp blue pencil to edit your wishlist.

Most of us would loath returning to a major city once we have left it.

Paris seems like the outlier, the superfluous destination. Why not stay in Spain? There's more than enough to enjoy there.

You are correct, this is a lot to get in. It's your choice: vacation or marathon.

Thank you for the reply. I agree that Paris is a problem. I will try and talk my daughter out of it.
If we did not do Paris, how would you alter the trip?
Thank you!

Don’t skip Cordoba.
There were some recent comments about the Valley of the Fallen on this forum. You should check them out. My own opinion is that a monument built with slave labor and, in part, intended to honor a fascist dictator is not something I would visit.
You seem to think that your travel days will also give you time for sightseeing. Probably not much. For example, 4/28. You will need time to check out of your hotel, get to the airport, clear security, fly, Get from the airport to your hotel in Paris, and settle in. I would either skip Paris or put it at either end of your trip. You could fly from Paris to Madrid at the beginning or fly home from Paris at the end. That way you’d elimiminate one flight and have more time for sightseeing.
Gibraltar has also been discussed many times on this forum. The consensus seems to be that it is not very worthwhile.
As to what you should see. . . Granada! The Alhambra is one of the most spectacular sights in the whole country.
Instead of Avila, how about Toldeo? Also reachable as a day trip from Madrid is Zaragoza, which we liked very much

I don't find the jaunt to Paris as concerning as the pace of the rest of it.
I would leave the day trips as mere possibilities, then make a real trip to Sevilla where you do not have so many one-night stays.

I would fly to Paris at the end and fly home from there.

Re: editing after taking Paris off the table—I'd just slow down in Madrid. Seeing Spain at an American pace means you see the sights, but are less likely to see the Spanishness. Also, I imagine your daughter would be able to join you for a dinner here or there during the school week, at least.

Though I'm curious, I haven't been to Gibraltar—no one speaks highly of it, and many people recommend skipping it. Every time I've tried to cram it into an itinerary it's been the easy/logical sacrifice for other priorities.

Spend more time in Seville, it is magical.
The beaches in southern Spain are NOTHING to brag about. I recommend skipping the beach.
You have an excellent plan, but didn't include Granada.

For me, the places obviously least worthwhile and cuttable from a short trip--aside from the beaches--are Avila, the Valley of the Fallen and Gibraltar.

As for the beaches, I suggest checking on expected water temperature to be sure your daughter will be comfortable swimming in early May (if that's why she wants beach time). Low 60s sounds cold to me.

One day in Seville is short. You need to find more time there.

You have less than a full day in both Toledo and Cordoba, also not ideal, but they are at least smaller than Seville.

In normal times (I don't know about this year) you need to get tickets ahead of time for the Alcazar in Seville to avoid a very long ticket line that stretches across and uncovered plaza; Rick's guidebook gives a workaround for the also-long ticket line at the Cathedral in the same city.

The one place for which you should get tickets well in advance, not just a couple of days ahead of time, is the Alhambra in Granada, if you can figure out a way to include Granada in your itinerary. Prior to the pandemic tickets often sold out more than a month ahead of time, leading to considerable gnashing of teeth and the need to buy $$$ tours (otherwise unnecessary) in order to get in. I see that 18 days in April already show low ticket availability, so it appears demand is increasing. All days in May, June, etc. are so marked, but I assume those months just aren't on sale yet.

The basic Alhambra ticket is the "Alhambra General" ticket for 14 euros. You wouldn't want the cheaper "Gardens, Generalife and Alcazaba" ticket because it excludes the #1 part of the complex, the Nasrid Palaces. The Night Visit to Nasrid Palaces is worthwhile, but I wouldn't recommend it as your only visit, because you only see the palaces, and there are other worthwhile sights. It appears that the Alhambra Experiences ticket gives you a nighttime visit to the Nasrid Palaces and allows you to see most of the other parts of the complex the next day, but it appears to omit the Palace of Charles V, which is a museum holding some lovely decorative elements from the complex (perhaps brought indoors to protect them from the weather??). I'd be sorry to miss that, but I suppose most tourists don't know what's inside that building and don't bother with it.

FYI there is a direct high speed train from Barcelona to Paris. You could consider flipping your itinerary visit Madrid area, then AVE train to Barcelona visit, then take the train to Paris and fly out. Makes more logic to me to be honest.

I agree with others about skipping Paris especially since FR has different COVID restrictions than Spain that could put a damper on that portion of the trip. Your daughter is young and will have many opportunities to visit Paris in the future.
Good day trips from Madrid are Avila, Valley of the Fallen, Segovia and Toledo but Salamanca is too far plus is an outlier so skip it.
I would take a train to Sevilla and sleep there and take a direct train to Cordoba for the day (30-minutes). I would also sleep in Ronda and Granada. Nerja is another outlier which I’ve never been but have heard that the Costa del Sol is ticky tacky with American fast-food chains on the corners.