You are allowed dig up/rotavate/landscape your garden in what ever manner you choose, in the same way as you are allowed cut branches that are over hanging, if the trees roots are on your side, you can cut them. i don't think its a liability issue, the trees would more than likely die or the growth would be stunted instead of falling over, and if they did fall, they would fall into his garden and not yours/mothers, then the liability lies with who owns them, obviously they were too big and fell over, he hasn't a leg to stand on as these trees are well know for there shallow roots and their ease of falling, this may sound malicious to some people, but its obvious from the original OP that the neighbour doesn't care what effect they have on ther neighbours so why should she, it seems they have tried to be reasonable and its getting them no where. IMHO i would do this if i was in your mothers situation.