how long are you going to your parents for? i  will miss talking to you on the internet, but i hope you have a nice time and a nice rest. 

Ne kadar ebeveynlere gideceksiniz? Internette konuştuğumuzu özleyorum, fakat umarim ki eğleneyip, dinleneceksin.

Maybe not flawless, but it´s as i would translate it, given my present knowledge of turkish.

Better might be:

Ne kadar ebeveynlerde kalacaksın? Not sure whether it should be ...lerde or ...lerle

and the ...siniz of the previous, is to formal ofcourse. Should be ...sin.

How long will you stay with your parents

Ebeveyn is a formal word for parent.  Anne-baba is more "feely touchy"

Anne babanla or Annenlerle  would be better

thank you .