I think you will find that, in an emergency roadworks situation, the various bodies that might have reason to dig up the road do not have a legal obligation to ensure that you can access your house by car. Whilst you can try and claim that damage to your car is their responsibility, I don't reckon it will wash - you could have found a variety of alternative places to park it - some safer but less convenient to you.
I take it that after the original emergency repair, they now wish to come back and do the repair job properly. For that they would normally give you notice - as they have done.
If the job isn't being complted in the timescal indicated, phone the local council (who are probably managing the job - but not the contractor) and ask to speak to highways, report your concerns and get a commitment for how long the job will take.
Complaints that could involve a claim for compensation will have to be put in writing.