Cornwall can either be really amazing or bloody miserable, depending upon your wet weather prep. As it is April, assume it will be freezing at night and rain all the time, so if the sun shows it's face, you will be pleasantly surprised.
You can be warm with campbeds or airbeds as long as you have enough layers. I usually have a roll mat, memory foam rolled mattress (but air bed works too), fleece throw instead of sheet, duvet and an extra blanket on top. It's also worth ensuring everyone has fleece pajamas/or dressing gown for mooching around in.
As you have young kids, I also recommend a portapotty or similar for the night - saves having to escort them to the loo at night, especially as you will be both be totally awake after the trip instead of half asleep.
Other wet weather tips: keep a builders bucket next to the zip door for shoes/wellies. It prevents mud being tramped around and you know exactly where the shoes are! I also rig a tarp with a windbreak next to the tent for a cooking area, so I don't have to worry about the weather when lighting a bunsen burner. To save on prep (especially with ravenous kids), I tend to buy stuff that can just be wacked in the pan - frozen stir fry veg with noodles, pancakes (make mix in milk carton and pour), chili con carne etc.
If you get an electric hook up, you can take a small kettle for the first cup of tea for the day. We have also used a small electric fan heater (no exposed elements), but we ended up too hot!