I don't know how or when am came to have this particular meaning, I'm afraid. Many Welsh prepositions have uses and meanings beyond their basic ones, especially in combination with various verbs, and this is just one example.
You have probably already met gwrando ar, mynd i, edrych ar, dweud wrth and perhaps a couple of others.
dihuno/deffro means both to wake up and to wake somebody else. This happens with several Welsh verbs - dysgu means both 'teaching' and 'learning', and benthyg means both ' borrowing' and 'lending', for example.
iddi hi = to/for her, and some other meanings depending on context.
I was marked incorrect for "Why are you wanting to wake her now?" I suspect that this might actually be correct?
The correct translation was apparently "Why are you going to wake her now?" I know that "am" can mean "want" in this context ... but does it also mean "going" = "intending"?