There are good ideas here. An extra thing could be to record the sound in case you want to demonstrate it.
The suggested sound-proof fence seems a good plan for the garden.
Also, people use thick hedging as a sound barrier, if you research it.
But the biggest thing would be the party wall. Lining it with soundproofing panels would not be not terribly expensive. They are used as standard in modern flats, and come in various thicknesses/ degrees of effectiveness.
For a comparatively small job like a bungalow party wall, it would probably be worthwhile paying the extra to get a more top of the range performance, among the standard domestic options.
( It's quite interesting, they go all the way up at the luxury end to be good for sound recording studios )
They look similar to a standard sheet of plasterboard, but are heavy because they are filled with sand. (So either use a soundproofing installer, or a builder who knows not to cut like plaster, because the edges need specially good taping to stop the sand pouring out at any join)
Can the party-wall room be cleared of anywhere for noise to break through? An open fireplace would transmit sound. There can't be anything but freestanding shelves, nothing drilled into the wall or even a 'butterfly' fixing on the board, for a picture, because breaking the seal breaks the soundproofing.
So would any continuous wood, which ought not to, but sometimes does, run from one half of a semi to the other. So have a search with a torch under the boards. It is easily remedied before the soundproofing, so the break between one house and the next is complete.
Are the windows double glazed?
(It might be necessary to line the party wall in the loft, if sound transmits up there. You can research and get advice)
The quality of your mother's life would be greatly improved. Instantly, she could try some noise cancelling headphones. They are not dear second hand, or someone you know may have some she could try. But she can't be expectedto live like that as more than a temporary fix. As you say, the bungalow is essentially unsaleable, so the work will need to be done sooner or later.
If the unfortunate neighbour is, as seems possible, funded by an accident compensation, her trustees will be able to repay the reasonable costs to your mother.
Whatever happens, recording the sound, and asking estate agents to value on a basis of it continuing, or being quiet, would show the financial price to your mother of being deprived of "quiet enjoyment" of her home.
The soundproofing measures would probably be reasonable, and a court would probably give an order that the neighbour's trustees must pay.
(Not that a court is ever a good idea, if possibly avoided.)
You don't sound anything but reasonable, and your mother really needs your help now.