You (or your mother if she's the named recipient) can safely ignore all debt collector letters. Debt recovery agents are utterly powerless to do anything. They are not a party to any contract allegedly breached by the driver.
The ONLY thing that DCBL or any other debt collector can do is to try and persuade the low-hanging fruit on the gullible tree to pay up out of ignorance and fear. You sound as though you may be primed to be plucked from that tree.
Never, ever enter into communication with a powerless debt collector. You can safely y ignore them. Nothing whatsoever will happen. No court claim, no bailiffs, nothing!
Another thing you MUST do immediately, is edit your post to remover anything that would identify the driver, such as the Keeper. For now, your mother, as the Keeper is the only person who can respond to anything. You can do it all for her, but it MUST be in her name.
Whether you are named person on the policy is irrelevant to anything and you should stop harping on about that. There are only two legal entities involved here... the Keeper and the driver. Whilst the Keeper could be both, ECP (the operator) don't know that and there is absolutely no legal obligation on the Keeper to identify the driver to an unregulated private parking company.
So, you can handle all of this on behalf of your mother, as long as you do it all in her name. If you follow the advice, there no way you will be paying a penny to ECP.
As the Keeper is now receiving debt recovery notices, it is far too late to appeal this. Please confirm that this is the first correspondence received about this Parking Charge Notice (PCN). You have to ask, why did the Keeper not receive the original notices. Invariably, that is because the Keeper never updated their new address for the V5C registration document. Whilst updating the address for the drivers licence is one thing, it is in no way connected to the V5C, even though the DVLA handles both.
Please double check that the address on the V5C is, or at least was up to date and correct at the time of the alleged parking contravention. If it isn't, that needs to be updated immediately and can be easily done online. Also, if it was not updated at the time, then the Keeper will have to submit a Data Rectification Notice to ECP. Whilst DCBL have found the correct address through a credit reference search, if the operator, ECP, hold two possible addresses, you can bet your bottom dollar that they will use the incorrect one to save any court claim which pens a whole new can of worms.
You need to understand that nothing we advise on will have any effect on anyones credit rating. There's no chance of a CCJ on anyones credit file. The ONLY way anyone could get a CCJ is by default because they did not update their V5C address and they knew nothing about a court claim. In any other case, if a court claim was unsuccessful, as long as the judgment amount is paid within 30 days, it is expunged from the record.
So, before we can move on to providing all the advice you will need to get over this, you need to confirm whether the V5C address is or was up to date at the time of the alleged contravention.