Hi Els,
If you need to choose between March and May I would go for May. I was in Andalucia in May this year - the weather was gorgeous during the day - bright and sunny. The flowers were out and there was still snow on the Sierra Nevada. It was still a bit chilly in the mornings and evenings. Normally Andalucia is very dry however this year it started raining on Boxing Day and did not stop until a month before I got there - there had been flooding and there was damage to the mountain roads.
The Italian lakes should be good in May also , the alpine flowers will be coming out .
It is always hard to choose.
Colin