Neighbor won't agree to share cost of replacing fence

[Account Closed]

We've owned the property about 6 months and have fixed a lot. Now it is time to fix the fence. The wood is ugly from weathering, it is literally falling down; a whole section of it loses attachment at either end, it has multiple patches from holes at the bottom. We talked to the neighbors, and on one side, he is all for it; he wished he could've done it with the previous owners.

The second neighbor said it isn't necessary. This is the side that is literally falling down. She said that only the posts need to be replaced, and she has a guy to do it for $400. However this is a bandaid on a bullet wound. Her property clearly gets little care.

1. What should I do?

2. Do I have legal recourse to obligate the next door's landlord?