This is what I would do
1. Call the hotel again and ask to speak to management staff and calmly explain what has gone wroing. They will have more time to look at this than the front desk who may also be juggling people stood in front of them. Say something like 'I think there has been a mistake in the billing of my stay'
2. If that fails call IHG
Only after you have done 1 and 2 and not has resolution would I consider a charge back. Your credit card provider will have expected you to try and resolve it yourself first.
They are your last and not your first port of call.