The Cornish coastline is pretty durable. As proven by areas with towering cliffs, the rocks don't crumble into the sea regularly, they are very hard. Both Rock and Padstow are low lying, just at sea level. I have lived in this area all my life (and I'm old!), and I can't see any difference in sea levels.
Have never heard of any private schools in either place, but neither is very big. The only one I know of is in Truro. Because of transport difficulties, a lot of private school children in Cornwall have to board. Don't dismiss state schools, Cornwall education is very good. We don't have the same problems as up-country with multi-cultural classes and lots of pupils that don't have English as their main language.
Pros: mild climate, laid-back way of life, wonderful scenery and places to visit, well away from the rat-race, not much pollution (in most places you can see the stars), low crime rate.
Cons; poor public transport system, property very expensive, wages low, very few opportunities for young people seeking work (most of them have to move away), not much night-life.
I think something you have to consider is that Rock and Padstow are both a long way from any large hospital if either of your parents needs hospital treatment. In the summer, an emergency can be a real problem if the lanes are clogged up with traffic, although the Air Ambulance can be called out if necessary. Most of our local GPs and nurses are wonderful, local treatment is much better than up-country.
Don't count on regularly taking your doggie to the beach. Dogs are banned from most Cornish beaches in summer.