From a friend - "The principles of law are, however, reasonably clear. Where the encroachment of tree roots [or branches] onto the property of a neighbour causes damage, this constitutes a nuisance, which entitles the injured party in an appropriate case to seek damages or an injunction or to abate (ie. reduce or remove) the nuisance himself or herself. Moreover, he or she need not wait until damage is done: he may take protective action by cutting the roots as soon as they project into his property...... I don't think you have the legal right to cut them....you could easily get stung. ...
Where a branch encroaches onto another's property and causes damage, the occupier of that property will have the same remedies as in the case of encroaching roots."
McMahon & Binchy Law of Torts edition 3, pub. 2000, page 687:
If this citation is accurate, then OP's mother may pro-actively cut the projecting branches. The citation of course may well be one those interweb things that gathers gravitas as it rolls around; caveat lector and all that good stuff.