Hello and thank you for your question.
The law in relation to fences is governed by the Fences Act:
Part two of the Act sets out when parties have to contribute to the costs of fencing, and essentially the law is that neighbours have to contribute equally to a sufficient dividing fence, but that if one neighbour wants something more than what is sufficient that neighbour has to pay. What is sufficient is a subjective question that will depend on the circumstances and is a matter for negotiation and by reference to other dividing fences between similar properties. It is not enough to simply say that wildlife keeps coming over from the other side.
On the other hand, repairs for damage to your property or to a dividing fence that is caused by the neighbour's neglect or the neighbour's animals will usually be payable by the neighbour responsible for the neglect. Neglect can include failing to prevent tree roots from a tree on your property from intruding into a neighbour's property or from damaging the adjoining fence. In your situation where you are asserting that their tree roots uplifted one of your trees which in turn damaged the fence, then you would be right provided you can prove that the real cause was their tree, however, that may be difficult to prove in the case you describe.
If after reading the above you believe the increased fence side is reasonably necessary so as to be merely a sufficient fence, then the Act sets out the procedures for claiming a contribution from the neighbour, but if they resist you may find yourself having to apply to the court.
Similarly in terms of the cost of repairs or damage to the fence and your tree, you need to either negotiate some compromise or apply to the Magistrates Court.
Unfortunately the processes will generally require the assistance of a lawyer as the law of negligence and nuisance, as well as that set out in the legislation will all have potential application and these are not matters that can be comfortably addressed by a person untrained in the law.
The following article from the Victorian Law Handbook may also assist your understanding.
Good luck and please rate my answer.