we had to pay out last year to get one of her massive conifer trees cut on our side.
Conifers are a real pain! Fortunately I have good neighbours. The neighbour to the left used to live next-door-but-one before moving to the house next door about three years after we moved in (a long time ago!). The garden was hedged all round and there was a privet hedge between our two gardens but part of it died, so the original neighbours planted about three conifers - even though it was our fence. We had put chicken wire all round the garden inside the hedges to keep the dogs in. We didn’t realise then how large those conifers would grow and over the years they have grown to such a height that they were keeping the sun off much of the garden by late afternoon. Eventually last year I asked my neighbour if she would mind me having the tops cut off, as although I’d had the branches cut back on my side it hadn’t solved the problem (or killed the trees!). Fortunately she agreed and it‘s my fence so I didn’t expect a contribution, but I was a bit peeved that we hadn’t even planted them! She has another conifer that’s not on the fence line, probably planted by the same original neighbours, but there’s nothing I can do about that.
Would it be possible to put sturdy wire fencing inside the boundary on your side to keep the dogs out and screen it with shrubs? It would be cheaper than wooden fencing and your neighbour would still have to replace the broken fence.