Neighbors threatening lawsuit on our dogs

Hi, One day out of the blue we received a text from a neighbor who yard touches ours stating they were putting their home on the market and asked we keep our dogs inside. We obliged. Long story short the house sat for weeks and the text message/call requests were endless. We wondered what the sudden weird fixation was on our dogs who are not excessive barkers. We have never gotten a complaint from anyone ever, including them, in all the years weve lived here or anywhere. We never leave the dogs outside unattended. They dont bark excessively. One day we received a FedEx that basically says that one day potential buyers were doing home inspections outside and our dogs and the neighbors dogs were out and "barked aggressively for 20 minutes" and the next day potential buyers cancelled the offer stating "aggressive and excessive dog barking" and that we either go to mediation or they are suing us, and the other neighbor, for: the loss of sale, relisting fees, carrying costs, etc etc. We were shocked! They wrote the letter in a tone as if all the times we were doing them a favor to keep our dogs in, that they had made complaints about the dog noise, which wasn't true at all, and said we were noncompliant with their requests (which we were compliant, despite being under no obligation to be, bc we are good neighbors). So immediately we call them and say we had no idea they had concerns about the dogs or felt they barked to much, what can we do? He basically explained that the potential buyers were doing lot line inspections along the fence with their realtor when the dogs supposedly (naturally) barked at the strangers on our shared fence. Then he went on to say he "would not talk and lawyer up." He did however say "we spent 1/2 an afternoon filming your dogs barking." So basically provoking our and our neighbors dogs to gather supposed evidence. So, we took initiative anyway and built a SECOND fence between our home and the neighbors home with other dogs so they cant see eachother or run the fence, and installed more cameras to be able to show they are lying about barking. So the irony is these neighbors moved into another home about 6 months ago when they started remodeling this home for sale. Also, they have had surveyors out regarding lot lines and another company out digging up lines all after the potential buyers walked away. Also they pulled the house off the market 3 weeks prior to even sending us this note and its still not relisted. So our lawyer spoke with theirs and he claims "everyone misunderstood the email" its not necessarily about $ as long as we go to mediation and hinted at the fact that we would have to make a written agreement regarding our dogs, so they can give it to potential buyers. Mediation of course would cost thousands and they are trying to put rules on our property that are beyond the laws already existing by the city, which is ridiculous! They have nothing to lose and we arent going to go to agree to something that alters our life indefinately when there is a good probability they will sell to normal people who may have their own dogs or enjoy the surrounding environment which is full of dogs. We also offered another bigger fence but the lawyer said "no because they dont want their sightlines blocked." What would you do since they are unwilling to speak with us or accept any of our proposed solutions?