If neither vehicle was insured you will have to sue the other party in order to collect any damages. Drunk driving is a contributing factor but really whichever party is At Fault for any reason will be liable to the other party. The bad news is that if the person did not have insurance the probably don't have assets to pay the damages. This is why you need insurance and uninsured motorists coverage.
It all depends on her insurance cover
The insurer (either your mother/father or both) are responsible for all costs.
If your child has a license the insurance on the car will probably cover it. The company can take the position that they were not supposed to be driving it and are not covered in which case it would come back to you because the child is underage.
As long as she has the correct insurance that allows the car to lent to a friend then it should cover you.
Actually, they are at fault, or so it's presumed - if their license is suspended, they shouldn't have been driving, hence, they should not have been there to have been involved in an accident. On top of that, they've voided their insurance policy by driving on a suspended license, so the expenses will likely end up coming out of pocket.
You will probably receive a citation for driving while suspended. If you were not at fault for the accident, the other party involved should have insurance that will cover your loss or damage that resulted in the accident. It is a good thing that you were not at fault in this accident.
When this happens, your Insurance company pays for damages. If the accident is your fault, your insurance rates can go up.
In the UK, if you are involved in a Road Traffic Accident that is not your fault but you are not insured for third party, the law assumes you are at fault and you may face civil action from the injured party. You may also face criminal charges for driving without insurance.
Your insurance won't pay for any damage or injury to persons or vehicle. (unless they were driving legally with a drivers permit)
The at-fault driver's insurance will pay for all property and bodily injury damages.
It would be no difference than if the people involved in the accident had different insurance companies. The coverages are the same so there would be no difference.
no insurance + jail