NTA. Talk to your neighbor and explain it’s a liability and you also don’t want to hear your dogs barking. If they continue to do it, you could get something like this spiky pet mat. You could put it on the swing, run a chain through it and put a lock on it. Ugly, but would probably do the trick.
I bought some plastic pot inserts from Amazon. They’re definitely hostile but they get the job done.
Cat Scat Spike Strips (24Pack) -... https://www.amazon.com/dp/B07YTPB7H2?ref=ppx_pop_mob_ap_share