Second this...;making your position crystal clear.. and yes as others have said tell them also that you will be making a social media stink over this too.Write to them & explain why you are not paying, that way you will probably avoid it ever getting to court. Ignoring them will only make things difficult.
IMHO, it's not a matter of right to do 'x' or 'y', but that your reasonable expectation was competent service, which obviously you have only gained from 2nd contractor. They have not delivered this, so their fee does not have to be delivered in return.
1st Contractor will have to consider if they can claim to have fulfilled their contract- to provide a service that most people would deem reasonable. Their T+C's cannot really function to undermine the main Acts that protect us from poor services/trades. I.e, there is no 'We reserve the right to be crap and get paid' -clause.