Hi Abi,
I don't have any iOS devices, but I have viewed billybirddesigns.com on my android phone and pad but do not see the problems you mention.
As with the other site about (see my screenshots) it displays well on both devices and in both orientations.
Android pad (ASUS TF101)
As a test, could you please manually remove this line from your published index.htm
<meta name="viewport" content="width=device-width, initial-scale=1.0"/>
And replace it with
<meta name="viewport" content="width=device-width" />
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