Emma,
First of all do not worry about your pigs being bored, they are not. You are already providing more than most people would, and much more than nature alone would - pigs in the wild don't get pilates balls to play with!
What they are displaying is very natural pig behavior, rooting around, spreading straw to find the heads and just being pigs.
Moving the ark will be because they can get their noses under and root. Now they have found that they can do this, they will continue to do it until you make it impossible for them. Many calf hutches have holes at the bottom and you should use these or drill some to then anchor to the ground using metal or wooden spikes.
As for spreading straw, this is probably as a result of a) the ark moving and b) you giving them far too much straw. Once the ark is anchored down, put some straw inside - only a quarter of a small bale. If still there in the morning add another handful. If they have moved some outside, then you gave them too much. You idea of cosy for a pig is like putting you in a sauna. Pigs need much less bedding then you would imagine, and are not polite - they just remove excess and dump it outside! Offer straw (put some inside) but don't be offended if refused (dumped outside).
Enjoy your pigs !