Legal Question in Real Estate Law in Illinois

If the fence is completely on his property, yes. If it is on the property line then the cost is shared. [A property line is a mathematical abstraction and has no width, therefore, the fence HAS to be partly on each property unless the posts are totally on one side or the other of the line.]

Your recourse is to put your dogs on long stake out wires. I know that this does not keep the children away from the dogs, but unless you are willing to put up a fence on your side of the line and pay for it yourself you do not have much choice. If you do that you would be giving him a few inches of your property because of adverse possession. IF you do put in a fence, -do not- remove his. He COULD sue you for vandalism, that would probably be his ideal situation - new fence, you remove the old one, and you pay him for the privilege.

Also, by asking him about the fence you have put yourself in a fairly decent legal position, but getting the refusal in writing would help you even more legally. Of course, if he is as smart as I think he is he won't reply in writing. If he did reply in writing that would be evidence that he was on notice that there was a problem and that he failed to take reasonable precautions. (From a Real Estate perspective he does not have to help with a fence, from a Tort perspective if he is aware of a potential problem and does not take action then he COULD be liable. It would be up to a judge to decide which of the two rules to apply - probably Real Estate.)

Your concern does you credit, but you can't force him, if for no other reason than because the dogs are yours. Even if there were no dogs involved you still could not force him.

If you can afford it, I would suggest that you put in a fence yourself just on your side of the property line. As usual, the best solutions are usually the most expensive. You have my sympathy.

Whose fence is it? You should have a survey from when you bought the property. If it is yours, then you need to care for it. If it is your neighbor's, your neighbor is responsible and if it is in such disrepair that it could cause injury, you should consider contacting your local building department. Your community may also have a "mediation" function when neighbors have disputes like this. Worst case is if it is your neighbor's and it is in that kind of disrepair as to be a potential source of injury, the building department may have the right to sue your neighbor to repair or remove it. If it is your neighbor's fence and it is partially on your property, you have the right to sue your neighbor to move it at your neighbor's expense, but expect a "survey fight". Alternatively you can put your own fence up on your own property and not rely on your neighbor's fence at all, but then you will be responsible for it.