A couple of things come to my mind.
First, you said a couple of times that the two of you "came to an agreement," but when you describe it, it sounds more like, she told you what she wants, and you submitted because she was grumpy, and you didn't want to cause any bumps in the "cordial relationship". I seriously question how cordial it is.
Second, does your dog protect your chickens? Or does he just run with the neighborhood pack? If he's protecting your chickens, then you should have less to worry about.
About the chainsaw, i'm going to be frank. I live in the country, and we're not zoned. I can run any business i want to out of my property. If my business had to do with a chainsaw, i wouldn't give a dang what you thought about the noise as long as i wasn't doing it during sleeping hours. And i don't think you have any business causing a fuss about that. Didn't you say there are 10 acres between you? How loud could it be?
One more thing. If you're dead set against getting a fence, there's a lot to be said for clearly drawn verbal boundaries between neighbors. We don't have a fence (YET) between us and our neighbors. But when their pit bull chewed through her rope and came after my chickens, i marched over to their house, looked the owner in the eye, and said, "If she comes after our chickens again, my husband will shoot her, and i don't want that to happen." After that, the neighbor put her on a chain she couldn't chew through. He knows where we stand. We make it really clear. And even though, we're not exactly chummy, we can keep the peace because our invisible boundaries are drawn clearly. And those kind of fences make pretty good neighbors too.
I'm all for friendly neighborhood/community relations and letting the dogs roam together (although for me, that's completely counterproductive if your dog's job is to protect your chickens), but when it comes down to it, if my chickens are off of my property, and something gets them, that's my fault. But if your dog is on my property, and he/she goes after my chickens, that's your fault, and i will protect my investment. I worked too stinking hard for healthy chickens and a growing flock to have a grumpy neighbor's aggressive dog ruin it for me because i want to "keep the peace."
If my dog goes after someone else's chickens (or whatever) on their property, i won't blame them for shooting her either. Fair is fair.
I think you need to stand up for yourself as to the dogs (that whole thing about you being responsible for puppies from her wandering in heat dog is ridiculous) and as to the protection of your chickens. And if you don't want a fence, well then, you've got to know what the consequences will be and lump it.