Neighbours tree

[Now we're 3]

Sorry if this isn't in the correct place. Looking for some advice as to what a neighbour "has" to do.

The subdivision of our area was done in a very strange way which has resulted in a little bit of land that backs onto the side of our garden actually being owned by the family that live at the back of our garden (but on the street above). Bit confusing I know but what is results in is this bit of land being unused and bit overgrown as they can't access it without climbing down a rockface or coming through one of our other neighbours garden. DH goes in and keeps things under control so doesn't look too bad.

However issue is that there are a number of very tall (we think they are campor laurels) that are dead. We had a arborist around to get a quote on cutting back our own trees a number of months ago and he commented that it had been a long time since he had seen a tree in that state. He provided a report stating this and also quoted to cut it down and we took quote and request to neighbours. She works away and first of all got a friend of hers to contact us who said that (1) in their opinion there was nothing wrong with the tree and it was perfectly healthy and (2) she was a single mum so couldn't afford to pay to get the tree cut down. We responded at the time saying she could get another report if she wanted to but was unlikely any arborist would say that the tree was healthy and we provided her with photos of the large branches that had dropped off it into our garden (in one instances smashing our washing line) and that we were requesting the tree be cut down as it was dangerous. She said at that stage they'd be in touch nothing happened and then we didn't follow them up either.

Well today we came back to find several really huge branches had dropped into the garden demolished one of our fruit trees, broken one of the wrought iron animals and punctured the cover on our spa.

We spoke to her son (she is on holidays in Thailand at present) and he said he would talk to her when she gets back and would be in touch. He came down and saw the damage and amount of tree that was in the garden and he acknowledged that it wasn't good.

Hopefully it will all be easy to sort out she'll come home and agree to pay for the new spa cover and agree to get the tree(s) removed. But if she doesn't does anyone know what our rights are and can we make her remove them? Given their height and that there is more than one of them it won't be cheap - possibly about $2K.

We won't push it until she comes back and gets in touch but is good to know what our rights are in advance.