I think you might need to live with it. Not what you want to hear but 3rd party warranties on used cars are pretty much a waste of money - they're loaded with small print excluding things and making claiming v difficult.
With the lights, were they working at the time you bought it? IMO That's something you should have checked & brought up at the time of sale, if the lights failed sometime after you bought it's hard to blame the seller, light bulbs do go pop with wiring & connectors going bad with age/heat cycle (prob not covered by warranty), and for £2250 I need to assume we're talking a car over 10 years old where wear & tear has to be factored into it's price
Likewise the engine, did it do this on test drive/as soon as you bought it, or did the issue only appear later? as that has a big impact on whether they have any responsibility over it - if it's something like say exhaust issues, fuel pump, bad spark/coil, mass air sensor, vacuum lines etc - all things that could potentially stall the car or mess with rpms, then almost all of this would likely count as wear and tear and almost certainly not covered by warranty.
I can't speak for the garage giving you the run around rather than being direct with you, some are sadly known for working that way - but considering both these issues v likely weren't covered by this warranty, the warranty has been refunded and you've already had them fixed elsewhere without now being able to prove them and we're also considerably past the point I believe you could return the car - what would you really be expecting them to do about it all now?
What was the issue that your cousin fixed btw?