Eucalyptus trees less likely to blow over in a storm due to their rubbery type branches. But could you maybe trim it back from your neighbours side? One point that you should be aware of though, I've noticed in more recent years when making application for the Annual Hse / Home insurance, one of the questions ask is 'Are there any trees within 40mts of the Property?' One can only assume such a question is asked, so that if a problem were to arise because of the root system, the Ins Co will cover their own - you know what - to get out of paying for possible damages. I'm having a sort of the same problem with my neighbour(s) and A Tree. When I cut it back, all 3 neighbours 'Claim' it to be theirs - it is litterally on the corner boardering all our houses. However, as I've said to each of them, who will pay for the damages should the offending tree fall in a storm and damage my house? So maybe it is best that you try and keep the eucalyptus cut back so as not to cause any hard-feelings.