Listen...don't get me wrong I love trees...but no one should have a big fat "forget ever seeing the sun again" tree monster imposed upon them

The only way you can justify trimming back trees is if the tree( s) poses any danger to your property. e.g branches posing a threat during winds or storms or that the branches are so close to a window that they could crash through them during a storm.

Ok so if you can't prove this...what do you do?

Unfortunately, you can't just cut off tree limbs and chuck them back over the fence. Trimming down branches from your neighbour’s side without permission is trespassing. (The only time you can legally trespass to chop down branches or cut down the tree is in an emergency such as fire where a lit branch can set your property ablaze.)

Ok so what are your options?

If you can get to the trunk of the tree, without your neighbour seeing you obviously, hammer in some copper nails.
The ions in Copper will rot a tree from the inside.  The tree should die within a year depending on how many you knock in

You can also use copper to rot out a tree stump!

Your second option which might be more secure is using hydrochloric acid. You need to drill a hole in the tree trunk and pore down a bit of hydrochloric acid. This will kill the tree and it will be difficult for your neighbour to prove that you did anything wrong.

You should be able to get the nails in any decent hardware/DIY store and acid by googling

Good luck and remember we need trees so this is only when desperate measures are called for!