Ok, I'll do my best to answer all the questions.
LIZS - the wall is under 2.5m on our side. On theirs, it is about 1m, as their garden is higher than ours. This obviously impacts on our privacy, Goblin, as anyone in their garden who walks along thier path is instantly overlooking our garden - even their 4 year old! We have not, however commented on this, as c'est la vie!
The frame will be about 1m higher than the wall, in part, set at an appropriate distance from the boundary, not jammed up against it.
We do not want to put the frame on the other side, next to other neighbours, as it will give us fence maintenance issues in the future (there is a waist height wooden fence on this side, which is our fence to maintain). It will also then block one set of steps down into the garden, which lead from our terrace down into the garden. Given the orientation of our house on the plot (and other neighbours house on their plot) , it would also box in this part of the terrace, which is not particularly desirable.
We do need a larger structure, given dd's age and size. This is something she will not grow out of needing/wanting/using, and so it needs to be a bit larger than standardly available ones, to give dd the head space/required heights to ensure safety. It is not enormous, and will be under 3.5m in height (legal requirement for where we are situating the frame is 4m). It is a standard playset, with a platform and slide, swing arm and a tower/house on the other side. Nothing outrageous (and much nicer looking than many i have seen) - what they will see of it is the top of the swing arm, and a beautifully built cedar shingle roofline, which will look an awful lot better than the grotty falling down shed it is replacing (at the same height)
They could chop down/cut back the trees outside their wall, as thye do belong to them (complicated arrangement whereby we all have a strip of land bordering our property which is for us to maintain - somethign to do with it being a 'no-mans land' so that the cows do not damage our fenceline).
It is not 'such a large structure' - it is big for our garden, yes, which is our choice considering the needs of our children now and in the future. But it will not be towering over their garden anymore than the shrubs which have just been removed have been (we checked - an elderberry has just been taken out which is higher and wider than the bits which they will see anyway)
I do take the point that relations might not be good in the future. They won't be if we don't go ahead, either. We have a swing and slide set that dd is already too big for - she cannot play on it safely. We need to replace it for her, so that she can play in her own garden. We cannot replace it with a standardly available commercial one, as they are the same size. The one we will be building is not hugely bigger, but is enough bigger for it to be safe for dd now and for years to come.
There is a potential compromise on distance from the boundary - I need to walk that through later on, as moving it further into our garden might end up compromising the steps on that side of our terrace (awkward bloody gardens round here!), but we will move it slightly if we can. We cannot place it anywhere else in the garden without still obstructing their view of the fields (which they want without actually having from their own garden backing onto the same fields!) or blocking in our terrace and compromising our own use of our garden.
Contractor went round earlier - his choice not ours! - to see if there was anything that could be done. They have said that they are apparently going to be clipping/chopping the trees at the end of their garden this year, so they will gain extra vista from there.