Families and money eh?
I'm inclined to agree with the other posters and avoid the sister's mortgage payoff. It may be a rational thing to do, but I suspect rational isn't going to get your mother across the line.
I'd get he to pay off the mortgage first. A) because its a guaranteed safe return that will drop her ongoing cost of living, b) because it won't impact her pension etc, and perhaps most importantly, it should be really easy to "sell" to your mum. It also nicely locks part of the cash away.
I'd then try the annuity argument. As they have just retired, do they have a super fund that is already in pension mode? If its a recent retirement, is topping that up with the remaining $110k an option?
Lastly, is there something that has been on their "to-do" list for a long time that they could make happen with say $10k of it? While it doesn't lead to an on-paper optimization, better that they blow a fixed amount and lock away the rest, than get frustrated with cold turkey and blow the lot?
At the end of the day, its her money, and she is the one that needs to sleep at night over what's done with it.
Best of luck!