I actually don't agree with the Telegraph's take on the 28 day rule as that explicitly excludes uses within the curtilage of a building. The article also concludes that the siting of the caravan for use a playroom would be accetpable because it would be akin to an ancillary outbuilding. That class of permitted development expressly excludes any structures forward of the principal elevation of the dwelling, which would rule out the front drive.
If the caravan is sited so that it would be within the permitted development rights as an outbuilding, and if one of the children only slept in their but carried out all other activities in the main house, it would be classed as an ancillary building to the dwelling and would be acceptable.
So the answer is - maybe! I'm a planning officer so this is not just my opinion, its how it would be assessed if your neighbours reported you!