is this good??

Looks good but if drop one place you’ll richer experiences in the remaining places.

Too many stops for 13 days.

Eliminate Palma on this trip.

A good itinerary for what? And for who?

I disagree that this you have too many different stops for the number of days of your trip. Four nights in Madrid is more than many tourists spend there--you may even be able to squeeze in a quick trip to Toledo.

I think you can spend a meaningful amount of time in each place to get a nice, brief overview.

You can take the train from Madrid to Valencia and sightsee in that city even on the same day as arrival.
Flying from Valencia to Palma is pretty fast and cheap. Mallorca is a lovely island with some fabulous beaches.
You could then fly up to Barcelona, another short flight.

You will certainly be introduced a little more deeply to the Catalán language (and history), and if you do not know what that means, you need to research about Spain a bit more.

¡Buen viaje!