In reply to Sara G:
Hi Sara, unfortunately the simple answer is no, there isn't, and all of the potential crags are anywhere between 45 mins and 90 mins drive from Falmouth. Perhaps the nearest, and most suitable, would be Trewavas and, although you could possibly get away with not using much trad pro in your anchor systems, the anchors themselves are few and far between, not always obvious, not always ideal (but the only option), and require a long rigging rope to reach between the anchors and the climbs.
Also, the climbing isn't necessarily the easiest for youngsters, despite there being a handful of Diff/V Diffs.
Not really selling it, am I?
Trewavas
There is a small climbing wall in Penryn, if your little monkeys need to burn off some energy, or when the weather isn't good for the beach (https://www.gpclimbing.com/), or a via ferrata in a local granite quarry (https://viaferratacornwall.co.uk/), also close to where you are staying.