When I travelled abroad with my 1yo in a buggy, I found that a wheel able suitcase was actually easier with the changing bag on the pram and I had rucksack on me and a small hand luggage bag on top of the suitcase that strapped on. The suitcase was way easier to manoeuvre around than the wheel bag I tried initially as it was prone to falling over and not as easy to manhandle.
If I'm honest, I wouldn't be taking a pram for a 3yo, partly because I think that it would be harder work and unnecessary for a 3yo,but also because Cornwall is a nightmare with a pram, for the hills etc.
I presume that the 3yo is out of nappies, so beyond the absolute necessary foods for travel down and any dietary specific foods, I'd be googling supermarkets and go to the supermarket once you've arrived. Or order an online delivery for once you've arrived. I've known friends to even order to a hotel room, tipping up with bottles of wine to get the minimum spend!
Re packing, only take one lot of beach items. When my child was a toddler I found roll up trousers fab, as could have as shorts or trousers in the same day. I have always found that patterned/pictured clothes fair better than plain. Opt for items that are easy to keep together, such as sunhats or caps that can be clipped/attached to your bag etc. Definitely take a couple of outfits that would be for much colder days with lighter layers underneath, it's always colder in the evenings and frequently so during the days.
For toys, I used to take a water book where there were activities and colouring that were revealed using the pen you filled with water and then dried and repeat.
Have fun.