I've had my plot since DC1 was born (almost 5 years). It will be a cold day in hell before I consider giving it up 
I love it and would happily spend the say there with a thermos flask, watching my plants grow... I had visions of idyllic pottering but DC1 hates the allotment with a passion and DC2 is a Velcro baby. So we don't go as often as we could - we go for easy, low maintenance plants and have had great harvests of the usual - courgettes, runner beans, pumpkins, broccoli, cabbages, raspberries - with not that much effort.
Re safety: there are some dangers such as sticky outy canes and overenthusiastic attempts at using adult-sized tools... but it's perfectly manageable. It's a shame the manager was trying to put you off. It sounds like he has a problem with children!
Things that work with us to keep DC1 entertained are: picnics, taking a wheeled toy with us to be pushed/ pulled around, playing hide-and-seek (so one adult plays and one gets to do some work), growing raspberries or peas in the knowledge that they will be entirely harvested and eaten by the kids on site. Other than that my very outdoorsy, hands-on DC1 has no interest in digging, growing, watering etc