Hi! K.I.S.S.
I tend to agree with td, and hk, but that still won't stop your neighbor from filing a suit against you.
Two items stand out to me 'bout this situation; A) Your neighbor seems the type to encourage an attack just by the nervous energy he exudes, and B) Did he come onto your property to hang that sign, and trap on your fence? If that's your fence, and he did, then they belong to you now. For one, those traps will tend to attract more stinging insects, and the trespassing.....Well that's another experience I can offer later.
After researching, and coming up with the following two links, I can envision him or one of his family getting stung, and then filing at least a claim against your homeowners insurance to cover medical bills.
His lawyer may talk him out of a lawsuit, but they'll still go after your insurance company. I talk from experience, when my Dad was sued when a friend of my brothers broke his arm on Dad's property.
This one is from a sister forum, read the whole thread, and don't miss the last post:
Can a beekeeper get successfully sued for a bee sting? - Beesource Beekeeping Forums
This one is actual case law. It starts out with bee stings, and includes spider bites:
http://classweb.gmu.edu/jkozlows/lawarts/10OCT90.pdf
In either case, again, what stands out is; “Did the landowner, bee company, or Inn demonstrate reasonable care or was it negligence that caused the accident?”
I do not mean to infer that you are irresponsible, but because of the litigious atmosphere of today's world, I would think that this becomes a CYA situation on your part, and you would have to show some responsibility by trimming the tree to try, and control the stinging insect population.
Therefore I offer these sites:
This one condenses the next three pretty well:
Pruning a Fig Tree: 3 Tips | DoItYourself.com FigTrees.US FIG Fruit Facts Brian's Garden: Pruning a Fig Tree
The main premise is not to over-prune.
My sympathies are with you, and your family as my family has suffered the slings, and arrows of neighbors such as yours.
k