Madrid is inland. Barcelona and Malaga are coastal. Sevilla is 80km from the coast. What you ask is like asking for Tucson/San Diego (or San Francisco/Reno) weather.
Do either of these areas tend to get rain during this time?
No!
The only holiday I found in searches for this time is Corpus Christie in Barcelona. Am I missing anything?
Yes! Toledo usually has big Corpus Cristi happenings.
Pentecost Sunday is 30 May. Pentecost Monday is a holiday
and it is the climax of Andalucia's
Feria del Campo. But you'll be in Madrid/Barcelona at that time ... too bad!
... we're use to dry overheated summer days and drinking water till you burst.
which you don't want to do in Andalucia (where you can expect daytime high temperatures in the mid-90's). As an alternative, I would recommend the
Cruz Campo (beer, that is).