"Your vacations are more expensive than my house at the lake."
Translation:Eure Ferien sind teurer als mein Haus am See.
How about this other sentence? Eure Ferien sind teurer als mein Haus beim (bei dem) See.
What is more commonly used Urlaube or Ferien?
They mean different things.
Ferien is what a child has when school is not in session.
Urlaub is what an adult has when he has days off from work. It's also the word for "vacation, holidays" in the sense of "going away from home on a trip".
According to my Linguee dictionary it should be spelt teuerer.
That is wrong.
https://www.duden.de/rechtschreibung/teuer#grammatik shows teurer which is also what I would say.
Also, do you have a screenshot of what you mean?
https://www.linguee.com/english-german/search?source=auto&query=more+expensive shows teurer to me.
(Or try this link if the first one doesn't work: http://pne.li/3kfPVh7 -- it's a query for "more expensive".)
Linguee actually offers both your link and this one https://www.linguee.com/german-english/translation/teuerer.html Plus the usual page of external source examples for both options. I actually used teuerer in my answer because I wasn't sure and had looked it up on Linguee, but was marked wrong. Sorry, not set up for Imgur.