You aren't going to get deals on airfare in June. That is peak travel season, and gets hot in Europe June and July and August. I just spent 3 months in Spain and 2 weeks in Portugal. I flew to Madrid, and took trains and buses everywhere. I did not buy a rail pass, it didn't make sense financially. Rail travel in Spain is cheap. I also took some buses which were very comfortable and inexpensive. In Europe they have a website called blablacar.com where you can find shared rides (in someone's car) for cheap! I know they are in Spain, not sure what other countries.
I have done this 2 years in a row, first time I flew into Madrid and out of Barcelona, this year it was round trip from Madrid. Vueling also has really cheap airfare sometimes around Europe. I.E. from Madrid to Malaga, or Malaga to Barcelona.
I would recommend purchasing the airfare as soon as you know the dates. That time of the year isn't going to get cheaper as time goes by, it will get more expensive. So, when you see a good fare, jump at it. The kids will have a good time! (Tell them to be very careful of their valuables. Young and stupid. Never set your back pack down next to you at a cafe!!!, Don't leave your cellphone charging without being right next to it. I had an unlocked cell phone and bought sim cards in every country I was in so I had cell service with wifi and text. Really cheap!)