OK, so this is clearly using the equipment in the activity centre and (presumably) the services of a qualified instructor to supervise the event at all times.
In that case, it is still as I suggested (the insurer will not permit this type of 'client' at this activity - perhaps because it is adjudged that excitable kids are not likely to behave as if they are interested in learning how to climb at a 'social' type event.
Either way it seems to be a policy exclusion - ask them.
Doubt that you can obtain independent cover at an economic cost for a one off, compared to the hiring cost. If they were really interested in offering this option, I reckon they would have obtained the cover and factored it into the price of the hiring for the event.