The area that you would like to visit - Exmoor - is rarely mentioned on this forum because most foreigners have never heard of it. It is VERY SCENIC but can be prone to bad weather on the higher land so make sure you choose a good weather day. I shall refer to this map:>https://www.google.co.uk/maps/@51.1001826,-3.363255,11z/data=!5m1!1e1
Basically, you have 2 ways of getting to Lynton before going back east. On the map, you will see Elworthy, Wheddon Cross, Exford & Simonsbath. The B3224 connects all of these places crossing the moors. The B3223 connects Simonsbath with Lynton. I would suggest that you might like to use this route when going outbound before returning on the coastal route via the A39. In order to reach this route, you would pass through Taunton - which can be congested. An alternative is to stay on the M5 to junction 26 and take the A361 towards Tiverton before heading north on the A396 and then the B3223 via Dulverton and on to Lynton. I did this road and it has many bends in the Dulverton area. (The ancient stone bridge > Tarr Steps - is just off this road near the village of Liscombe - down some narrow lanes).
On the return via the A39, I would suggest you stop at Lynmouth and also look out for Selworthy - just a short detour left off the A39 as you approach Minehead. In Minehead, drive around to the old harbour. Dunster is very scenic but does attract the tourist hoards.
On your return to Bath, leave M5 at J22 and follow A38 turning off for Axbridge - drive into the middle. Then proceed to Cheddar and drive through the gorge before taking B3371 to join A368 for the final bit back to Bath.
