I don't believe one land owner can force another to pay for something that one wants, and the other doesn't want. You do not have to have a fence if you don't want one, so it's on him to pay for it.
I only have one neighbor to deal with. The other neighbor is across the creek, and the middle of the creek is the boundary. He decided to fence in some of his land, and he hired a guy to clear the fence line, then a crew to install 5 strands of barbwire. He went right to the property line and left my trees alone on my side, but didn't fence in two other sides of our mutual boundary. My place is shaped kind of like Home Plate in baseball. He cleared just enough to get the fence in and drive down one side of the fence.
He should have cleared more land because the pine trees are constantly dropping branches on his fence and destroying it. He spent a lot of money, but then decided that he didn't want to deal with cattle, so it's just something that he fixes all the time.
I'm in the process of fencing in all of my place. I want the fence to keep coyotes and hogs out. I realize this is impossible, but I will still try very hard to make it as difficult as possible for them to get through. I have his permission to clear the trees on his side of the line far enough away to never be an issue for the fence. He gets a free road, I get a fence that will not have trees falling on it. I set a corner post at each corner before clearing the land and eventually, I'll run a wire from corner post to corner post to know where my fence will go. I'm paying for all of my fence because I want to do it my way, and not deal with what he wants. My fence will be better then his and I will build it right next to his 5 strands of barbwire, which is useless at keeping hogs and coyotes out.
Having his permission to take out trees on his land is priceless to me. I wish he had taken out the trees on my side when he put up his fence, but at the time, I never thought to say anything.
With your neighbor, if he clears your trees so they do not damage his fence, then somebody is going to have to mow that area at least twice a year, or it will grow back thicker and nastier then before it was cleared.
Bulldozers are probably the very worse machine for clearing land, or anything. The mess they create is the hardest to clean up. An excavator is the best if you want the roots removed and clean dirt left. Grinding it up is the fastest and easiest, but it they do not like metal posts or wire. What he does on your side of the fence needs to be 100% in your best interest. It is real easy to create a nightmare of a mess with a dozer. And even if an excavator is used, there will be massive holes in the ground where the root balls where. You want them filled and compacted before the fence is built!!!!! If they are not compacted, they will turn into quicksand after it rains a few times. You never want to drive over a soft filled hole after it has gotten soft from rain.
Be sure to know 100% where your corners are. Once the land starts getting cleared, everything will look different and you will struggle to know what is where. This is why I set my corner posts. They are in concrete, they are wrapped with surveyors tape, and they are very obvious. I'm doing all the work, so it's on me to make sure I don't damage my corner posts. Whoever he hires needs to understand that the corner posts are sacred and to NEVER be damaged.