240,000 can buy a $1500-1600 per month annuity for a 74 year old. Not inflation adjusted. So in terms of reliable income, she's got maybe $2200 / month available, and if I'm reading this right, she's spending $3400 / month.
That move to a LCOL area might be an imperative - particularly if she insists on continuing to support the son, although the real solution is to remove the leach, as even in a LCOL area, someone bent on spending another persons money gets real expensive. Also needs to consider applying for welfare benefits / food stamps and so on - in this tight of a situation, a few hundred dollars per month can be a big help.
The other thing is, time is of the essence on getting the budget to balance - every month she's drawing too much will make the austerity that much more difficult to deal with. At 74, her life expectancy is around 13 years, although you may know more about the health situation that would make you think it might be longer or shorter than that. If she can adjust lifestyle further today, she can probably make this work more to her liking, but if she waits even 1 year, she may burn through enough of her nest egg that she has no choice but to take you / your brother up on your offer.