This is a tricky one. I feel torn about my answer and this is why: (long, sorry)
I bought a house that had loads of massive trees at the bottom of the garden. They were at least 50-60 years old or more, they pre-dated my house, but were incorporated into my plot iyswim, and they most certainly predated the new housing development had been built at the opposite side of my garden about ten years before I moved in.
Those houses all had gardens that were constantly in the shadow of the trees, which had had TPOs placed on them before the houses were built. The residents were constantly ganging up and petitioning me (and the previous owner) to pollard them severely every two years at my own expense. 
They gave all sorts of reasons about roots, safety, falling branches etc, but the bottom line was they just wanted sunnier gardens, without any falling leaves, and to be honest I couldn't blame them - so would I! They all had typically small, new build postage stamp gardens, whereas my garden was massive so the trees at the end did not bother me.
The previous owner had warned me that this would be an issue, so when they all came mob-handed a couple of months after I moved in, I took legal advice and told them that as I had the appropriate insurance and I understood that I had a duty to check the trees periodically to make sure they were not about to fall over, I was quite comfortable with the potential 'risk' and my position re: liability.
As far as their rights to have more sun in their gardens went, well they had none. The trees were already extremely mature when the houses were built - no-one would have viewed those building plots and not understood what they were buying into.
I said that I was happy to have the trees pollarded by a qualified surgeon of my choice every three years or so, but that they must club together to pay for it all, I would not pay a penny, as it benefitted me not a jot, and I had no obligation to them whatsoever. They agreed to this. All good. To be honest I think they already knew all this from the previous owner, but they were hoping as I was new I would be uninformed, and be a soft touch. Wrong.
However, I must say that nothing annoys me more than people who plant potentially large trees in inappropriately small gardens, or in inappropriate positions that will one day impact negatively on a neighbouring property. (not the case with my trees as it had been fields/woods before the houses existed.)
Not talking specifically about your mother here, but hypothetically/generally:
It is selfish and short-sighted to do this. If you have a biggish garden and you choose to plant a tree on or near the boundary in a place that will have more of a negative impact on your neighbour than it has on you, then that is just rude imho. and even worse if you've chosen a tree that will ultimately be too big for your garden, especially if you've put it near a boundary.
When I lived in a semi my NDN once planted a lilac tree slap bang down the (invisible) unfenced boundary between our two houses, about five feet from both our front windows. Luckily we both moved before it became large, but if I had wanted to stay then within about 10-15 years I would not have been able to see out of my own front window.
The roots can suck all the life and the moisture out of the soil making it impossible for them to cultivate any plants of their own, they greatly reduce the life/effectiveness of boundary fences or walls, and they get under the house or shed and cause problems etc. The neighbours have to live in a shadow not of their choosing but of yours, and they constantly have to pick up leaves that don't belong to them. They are entitled to prune off any overhanging branches but then they risk looking at a lopsided awful looking specimen, and you end up sulking with them for wrecking your tree. 
Of course if you got a TPO on it you can prevent them from even doing that very regularly or easily.
As to the question of 'rights' and 'fairness' and the fact that the tree was there before they moved in - well yes I see that point - sort of. But the tree was presumably not there before either house was built, and did not have a TPO on it preventing removal once it clearly became a poorly positioned pain in the neck. (if indeed it is.)
I am not going to say YABU, because obviously I don't know the exact size and positioning of the houses/gardens involved, or the positioning of the tree in relation to the neighbour's boundary, but if they can hear your mother coming into her garden and she can hear them talking about it, then I am going to assume we are talking about smallish gardens and an annoyingly large tree. If it is genuinely not impacting on them at all, and they just don't like looking at it, then I'd say YANBU and they can get stuffed.
But if it is impacting on them negatively in a way that it tangible and understandable, then I'd say perhaps they have a point. If your mother planted an ill-judged choice of tree, or perhaps a great tree but in an ill-judged position, then whilst she doesn't have to do anything about it, it would be nice if she would consider it.
But conifers don't respond well to pruning = it would look awful. It would probably have to be removal or nothing. Maybe she could agree if they paid for it.
(only if there is a case for her being at fault and them being genuinely inconvenienced though.)