Ok a few other idea.
you could add dirt to the
fence line effectively creating a ditch and then you could have the "ditch" lead to the pond.
You could also offer make an offer to the owner next door to plant them a garden like the one you have.
And they will have all the vegetables and fruits they want, make sure you have a non-crazy garden and that you share with them.
Then once they say YES to the offer you can then do the ditch thing with it flowing into your pond so that they are not worried about it going in their basement.
You could just skip all this and be upfront with them and even offer cash/free lawn mowing(
compost for you)/vegetables for them to let you build the ditch.
If they recently added soil to there yard causing this "new" flooding you could let them know that your insurance company is going to come after them.
So they
should just let you do the ditch and avoid all the complication.
So, let them know that the extra water will not be going in their basement but in the pond.
Let them know that if your house have damage they may be legally responsible and that you can help them avoid that.
Let them know that there is money/food/free service in it for them.
I really dont see why they would say no, unless you guys have a super bad history.
Just work your way up to it and ask. Maybe at a holiday/easter/party/cookout/few beers.
They are only human "RIGHT"?