I HATE my parents penny-pinching!
They wouldn't even let me buy one of Robb's DVDs!
Wow your parents won't write a check for 4,000 since you would need a chaperone, plus tickets or gas to get there, plus the other two meals each day and souvenirs.
You are right they seem very ilrational to me.
For any interested for 2 people to go to the UK and Sweeden my total came to 7,000 not counting the 3 extra days in London. We were extremely frugal and it still came to that. I am just saying be prepared.