Currently our family home is empty (furnished) and on the market while we rent a tiny place 3 hours away due to work, illness etc etc....life took a weird path last year!
Anyway, our back garden is a corner plot and we have about 4 houses back on to us in small sections. The garden is big and in one corner we have a shed and a small alcove where ds5 has his trampoline. The rest of the garden is mature and full of trees / bushes.
The neighbours that back on to that section of house have gone into the estate agents today ranting and being really aggressive saying that they don't like the trampoline being there, it's an eye sore and they want our new address to contact us directly about removing it. The estate agent refused and said she will pass a letter on if necessary. They got more aggressive and said they will make it a grievance and we will never sell our house etc.
There is a usual height fence and they can see maybe 30cm above it although I'm pretty sure their shed is in that region as well. They already contacted the estate agent once to say the trampoline was touching their fence and ds drove the 6 hour round trip thinking it was bad weather and movement.....it was over a foot away from the fence 
waste of a trip.
There's no where in the garden to move it to without it sitting very awkwardly and obstructing bushes, we've nowhere else to put it and it can't come here as we don't have a garden and I'm inclined to think, it's my garden, we can put a trampoline wherever we like. Just because we aren't living there doesn't mean they have control over what we do surely. It's not illegal to put things in your own garden even if neighbours may dislike is it?
It's not on purpose but our alternative is disposing of it but ds is desperate for us to get our forever house and have it back.
I'm a bit with these neighbours as when a fence panel fell down and we were waiting for it to be fixed, I looked out of the window while feeding ds and the wife came through and was wandering around our garden looking at plants and when I asked her to leave she came to our back door and tried to talk to me about why she was allowed to come on to our property.
Are we unreasonable to leave it where it is?
Ps estate agents are fine with it there, doesn't affect selling as it's a big family garden and looks neat and tidy tucked in the corner etc.