Experience / Advice with rejecting a car that was part of a part ex (CRA2015)

This is in regard to England.

TLDR; A friend has stated to a trader that they wish to reject a car (within 31 days) they purchased in a part ex with their old car. This complicates matters and I have advised them what to do and drafted them a formal letter of rejection to use.

Does anyone have any extra advice to give here?

The jist is that my friend has recently bought a car via part ex from a seemingly well to do with specialist dealer of said vehicle type.
Upon finding undisclosed issues as soon as they drove home in the vehicle, and upon some basic inspections myself that evening (at least 6 issues, 4 of which more major engine issues). He eventually went from going the route of requesting repairs etc. via CRA15 (with professional independent specialist inspection with report and evidence provided), to wanting to outright reject the car.

The context being the email (stating in a CRA15 manner, the issues and wish to have them repaired) was sent yesterday, the trader called my friend today, in a shall we say less than nice manner - claimed they were aware of the email but did not

have time to read it. During this call and likely in quick response to the nature the call took on - my friend verbally affirmed they wished to reject the car.
The trader did not take this well. They essentially refused in other terms.

After speaking with my friend, I drafted him a clear CRA15 formal notification of vehicle rejection.
Stating what they require to resolve this situation:

- Return of the traders vehicle
- Return of my friends vehicle
- Return of an inventory of spare parts for my friends vehicle
- Reimbursement to the trader of a sum of money paid to my friend for remaining value of their vehicle in the trade

l've dealt with a similar car CRA15 situation last year with myself. It ended amicably. However, this situation seems to be more complicated due to the fact that it is a part ex situation and the fairly considerable cash value of vehicles involved.

My friend is understandably nervous and stressed, mainly due to the fact that his (quite lovely) car is currently in their passion along with a number of parts.

An odd twist is my friend still has the V5C (for his old car) in their name.

I know this should be cut and shut, but due to the nature of this purchase and the dealers initial behaviour. I was curious if anyone had any experience or advice?

Thank ya!