ivy

well you could be really devious and spray the ivy coming onto your side with a highly toxic weed killer, I'm sure by law they are responsible for retaining their ivy if it is causing interference so you could talk to your local law authorities about it.

Apart from that I really can't think of any thing else, I have plants interfering from my neighbours side too, however I have no problem taking the hedge trimmer to them.

If it's splitting your fence, why not send them a bill for the repair of the fence or the renewel of the fence, I'm sure that would get their attention.

if you do cut it back remember to give the cuttings to your neighbour because they belong to them, its a shame youve got to put up with that sort of neighbour. good luck hosta :-)