But she needed urgently to convince her sister not to go to the police about the thefts from their mother. I think we need to see that entire email as a carefully-judged piece of writing aimed at persuading her sister not to take the obvious course of action, so any detail included is there for a reason, not just from an excess of candour.
Why might she have confessed to also stealing from her in-laws?
To add to the sense that she's definitely got a police record, and if her sister goes to the police, on top of the theft from Martin Hemmings, there's also another major family theft that might come out, maybe? So if they shop her, she's definitely going to jail? It gives her sister the impression that she has all the power, but then tries to stop her using it by saying, essentially 'You will be sending me to prison if you take action'.
To make it sound more like a form of compulsive illness, over which she has almost no control?
Or even, by pointing out that she's also stolen from TW's parents, and MH, lessen her sister's sense of grievance that their elderly, not well-off mother was her sole target?
I don't know, but maybe worth noting that it did work, and her sister didn't report it, although there's no evidence at all that SW tried to repay any of the money, despite all her protestations.