How to best incorporate Wales and Cornwall, from London.

I would normally not advise doing the 2 areas mentioned as it involves quite a bit of travelling and parts of Wales - especially Pembrokeshire & the Lleyn Peninsula - which is SW of Caernarfon, are rather similar to Cornwall. https://www.visitsnowdonia.info/llyn-peninsula
One way you could cut down on the travelling is if you could either fly into or out of Manchester to wherever you come from in the world and then use a London airport in the other direction so that you can see relatives. (Manchester is the nearest big airport to north Wales). From Manchester Airport, you could take a train to Chester for your first night - in this interesting English city near the Welsh border. Alternatively -go to Chester by train from London - if that is your starting point.

From Chester, I would take the train to Conwy and see that Castle & perhaps stay a night or 2. (Nearby Bodnant Gardens is well worth a half day & Llandudno is worth a look). Now, to continue, you could hire a car & drive to Caernarfon or take train to Bangor & then bus. If using a car, you could drive through the mountains between Conwy & Caernarfon but if wary of driving on the left - stick to the A55 expressway & coastal route. The Welsh Highland Railway from Caernarfon to Porthmadog provides a way of going through the mountains without using a car. Perhaps overnight in Porthmadog? https://www.festrail.co.uk
Just south of Porthmadog > https://portmeirion.wales

From Porthmadog, the Cambrian line goes south down the coast (very scenic but slow) and you can go all the way to Shrewsbury.
https://www.scenicrailbritain.com/lines/cambrian-lines
From Shrewsbury (worth a look), you could take a train down to Cardiff for maybe 2 nights. If you are driving down though Wales, just follow route A470.

From Cardiff, through trains go to Cornwall but these are slow stopping services. It is possible to transfer at Bristol to express trains to Cornwall. When done with Cornwall, direct train back to London (Paddington). Of course, you could do the whole thing in reverse and swap my suggested train legs for using a car.

For the longer distance trains, you will fond cheaper advance specific train fares get loaded around 11 weeks ahead. (short hops stay the same). Trains - www.nationalrail.co.uk
On some routes, it is cheaper to split the ticket - this site will tell you where this works out in your favour > https://www.traintickets.com

Long distance bus routes in Wales (free on weekends):> https://www.trawscymru.info
This site is good for finding bus routes:>https://www.traveline.info

Might flying help? London to Newquay (Cornwall), then see if you can fly Newquay to Cardiff or Manchester, sure you can fly Exeter to Manchsster. Would need to do a bit of googling....

In addition to Emma’s question, where in Cornwall are you going? Due to the many narrow , often windy, roads, it take longer to get to places than one would think. Some towns are better served by public transportation than others. Personally, I’d rent a car from the airport upon landing. Taking a train to a location closer to where you’re going, then rent the car, or use public transportation for the entire trip could be possible. Are you stopping at other locations or strictly visiting Caernarfon and Cornwall area?

In answer to your question, we have 11 days for this trip!

Caernarfon Castle is in Northern Wales. Yes, Northern Wales is great, loved Conwy.
However, you could do South Wales, which is equally compelling, then do Cornwall.
Do Cardiff Castle, the Museum of Welsh Life and other castle in South Wales. Tenby and St. Davids are great spots to visit. The scenery in South Wales, is wonderful.