Hi Squatchette
You are racking up bailiff's charges by not dealing with this. Even if you get your exemption as a full time carer backdated and the council tax bill goes away the bailiffs will still want their costs.
I don't advise that you answer the door and make sure all windows are fully closed. If a window is open they can call the police and the police can supervise them accessing your home.
You need to urgently talk to the CT people. Find out exactly what you need to do to get the carer exemption reinstated. If you can't get them on the phone they are obliged to have a formal complaints procedure. Their web site should give you details.
Also copy the complaint letter to your local councillors and to your M.P.
As for your car - I'm not sure as there is HP on it. Usually when a loan is tied to a car there is an amount that has to be paid back and once that amount has been paid then the car can't be re-possessed. Presumably after this amount the car is considered to be yours and the bailiffs can take it to cover the debt? Check this though as is just conjecture.
Has the car been adapted for disabled use? Bailiffs cannot take anything that is essential to your job or to the home (e.g. they can't take your cooker). So if it's critical to your daughter's need they can't take it. And if they try threaten to get the local paper round. They would leap on a story like that.
In answer to the question about having been to court - the answer is yes. This will have been to obtain a "liability order" against you prior to this you would have had to have at least a bill a reminder notice and a summons.
I appreciate that you have been trying to contact them but it really is CRITICAL that you talk to council about this. Go and sit in the waiting room and create merry hell if necessary. Demand to speak to a manager. Take everything you have with you.
The next stage (if the bailiff can't get entry a couple of times) is that he returns the warrant to the council and they start committal procedings so please please please deal with this.
hth