@Edw***
this is the thing though, in Chiang Mai at least, crutches will not get you a medical extension. You need to be literally stuck in a hospital bed. I have heard reports before of people turning up to immigration with broken legs in a cast and being refused. Generally, medical extensions are for really serious stuff, they don't typically hand them out to outpatients.
An agent familiar with your particular immigration office may have a good understanding of exactly what they need and may be able to present the application in such a way that it gets done. I'm suggesting this particularly as she has already been rejected with her hospital letter, what she has clearly isn't sufficient to do it on her own.