I dont think it is at all clear that the money didn't come from Emma's mother. Often a woman's fortune was settled to go to her daughters after her death or on their marriage. JA refers to Emma as "rich" and I feel that this means she already has £30k not that she has to wait till Mr W dies to get it. We are told that the Woodhouses are rich from "other sources" even though they have not got much land.
She will probably have trustees, to manage her fortune even when she comes of age, but I think it is "in her possession"... Possibly her mother brought a large fortune to the marriage and it went to her daughters after her death so Isabella has got her share on her marriage..
Em is unusual in Austen's heroines in that she IS rich.. she has no financial worries and doesn't ahve to think of what will happen if her father dies and leaves her less well off, or if she has to consider her future husband's fortune...