Hotel refund

Crownlyn

We were recently on a flight from Gatwick to Las Vegas, our flight was due to depart on Tuesday 15th however we sat on the plane for 4 hours and then was told the flight was cancelled. Was given an option of flying 2 days later or a full refund. We chose to fly 2 days later which wasn't ideal and spoilt our trip a bit as we had things booked plus the costs of returning home for 2 days but I'm not overly worried about that.
It was a package holiday with BA which included flights, luggage, airport transfer and hotel for 7 nights. 
BA are refusing to refund the 2 nights that we didn't stay at the hotel due to the flight cancellation. We didn't add on the 2 nights at the end as we had to come back on the original flight.
We paid for 7 nights but got 5 nights, surely they should refund this, we had two rooms for 3 people so we paid for 2 rooms for 2 nights.  BA also won't provide a breakdown of the flight cost and hotel cost.
We have received the UK law compensation that was due to us which they know they can't wriggle out of.
Can anyone advise or have been in the same situation. I have looked at CAA but it's not that straightforward to use.
Thank you

Voyager2002

They should have put you on a flight the same day or at least the following day, using a different airline if necessary. 

Crownlyn

Voyager2002 said:

They should have put you on a flight the same day or at least the following day, using a different airline if necessary. 

They didn't give us that option, just two days later or a refund. I know others got offered a later flight from Heathrow which they missed as our luggage took over 2 hours to come back to the baggage reclaim area. I just want our money back for the hotel really.

eskbanker

Crownlyn said:

It was a package holiday with BA which included flights, luggage, airport transfer and hotel for 7 nights. 
BA are refusing to refund the 2 nights that we didn't stay at the hotel due to the flight cancellation. We didn't add on the 2 nights at the end as we had to come back on the original flight.
We paid for 7 nights but got 5 nights, surely they should refund this, we had two rooms for 3 people so we paid for 2 rooms for 2 nights.  BA also won't provide a breakdown of the flight cost and hotel cost.
We have received the UK law compensation that was due to us which they know they can't wriggle out of.

You effectively need to treat BA as two different entities here.

BA, the airline, as the operating carrier, is responsible for paying out fixed tariff compensation for the cancellation (plus certain expenses if applicable), under the UK261 flight delay/cancellation regulations.

Separately, BA Holidays, the package provider, has liabilities under the Package Travel Regulations, so if you paid for seven nights and only received five then you're due a commensurate price reduction:

(2) The organiser must offer the traveller an appropriate price reduction for any period during which there is a lack of conformity, unless the organiser proves that the lack of conformity is attributable to the traveller.

https://www.legislation.gov.uk/uksi/2018/634/regulation/16