How to get refund of duplicate hotel charge?

cagsd

I booked a 3 night hotel stay in Germany via Hotels.com.  It was listed as 'pay at hotel' so we didn't pay upfront. The cost was around €320.
They didn't ask for payment when we checked in, so I presumed it would be pay on checkout.
On the last day (21st Dec) we went to reception to hand back the key and settle up. The receptionist was chatting to us for a few minutes before asking "do you need something else?" I then said we were waiting to pay. He advised, in broken English that, as we had booked via Hotels.com we would have paid online. I knew we hadn't paid already but assumed he meant they would take payment that way. 
Fast forward 4 days. On Christmas night I'm sitting watching TV with the family, when I noticed 2 push notifications from my credit card company, each for the same transaction (3 nights hotel at the expected price, plus a non sterling transaction fee). 
I tried to contact Hotels.com the following day via their chat service but they were beyond useless and basically didn't want to know. I got the impression their customer assistants don't speak English as a first language and really didn't want the hassle of helping me. I then emailed the hotel directly to ask for a refund of the duplicated payment. 
It took 3 days for them to respond, and all they said was 'please send us your credit card details so we can issue a refund '. 
This was 29th December and I've not heard another peep from them, despite me emailing 2 further times to chase up the refund.
It's almost £300 and I could well do without being that much out of pocket.
So, after my Ronnie Corbett esque tale, my question is:-
How on earth do I get my money back????? Not quite sure where to turn!!

eskbanker

If the hotel is unresponsive then you should be able to initiate a chargeback claim via your credit card provider for the duplicate charge, although it might be a bit premature at this stage.

Westin

Are they definitely both charges?  Are you sure one is not an authorisation for the charge?
Speak to your credit card company to confirm only one debt charge taken.

zagfles

You seem to have gone into panic mode over a notification, contacting them on xmas day? Notifications are often misleading, whenever I used pay at pump with my Santander card it would notify me of £120 spend, then the actual amount spent, then another £120. The last one was actually a refund/cancel authorisation of the first. 

Have you checked your account online, are both payments showing as taken (NOT pending)? 

cagsd

Yes both payments were definitely taken, not just pending. My credit card balance is approximately £560 but should only be £280 (allowing for the non sterling fee).
I wouldn't say I was in panic mode - it's now 15 days since I checked out of the hotel, and a week since they last responded to me.
I will contact my CC company tomorrow.