I think that your account has been compromised already either as a result of loosed password, exposed wallet key or the exchange in charge, I dont know how trust worthy the exchange is because I have never used them, so I would not easily accused them of stealing your fund, it might not really be them, which I am quite sure that you have let your key loosed to people around you and one of them must have been tampering with your account.
What I do not understand is that aspect of moving it to another wallet, the wallet in question, do you have access to it as yours? If you still have access to it and you are not certain of what happened, I think that you should just create some new wallets that are more secured and then you put in those coins into them.