It's sounds stupid, but if you stack timbers or do anything else to change the drainage in a way that results in more water on his property - even if it's the water falling on his property - you will lose in court if he sues. And there's no such thing as a plant that will take up enough water to mitigate a situation where there's too much water. Where's the water going to go?

A landscape designer is your best place to start, but we're not miracle workers. Good luck!

Doesn't make sense. So water can run on her property and it's Ok, but changing things to run on his property - may be a court case. Pls clarify. Are the 2 rain barrels his property?

Well didn't I say it sounds stupid? But yeah - I'm not a lawyer, but the way it's been explained to me by lawyers, engineers, and landscape architects is this. If you change the existing, established drainage situation in a way that negatively impacts a neighboring property, you can be liable for damages. You can't improve your drainage by screwing with someone else's.

In this scenario the first thing I generally suggest is going to the town, but it sounds like that's gone nowhere. To the OP - is it a utility easement or a drainage easement? What's downhill from you?

also, old railroad ties are soaked in creosote, they are the furthest thing in the world from eco-friendly! Put it like this: when we do a job that involves removing RR ties, I bring in another company to do that because I can't find a landfill or transfer station that accepts them near me.

The 2 rain barrels are on his side of the fence. My garage (and presumably his) are on our respective property lines. Between us is a 10ft utility easement with a fence down the center. I hadn't considered possibility we could go to court over doing something that kept as much of his water in his own yard, so to speak, because I'm not trying to add to it - just prevent or slow it from coming into mine. For argument sake, let's assume that from when I met briefly with the village, they told me it's ok to landscape back there so long as I know the utility company could tear it out if they needed access to the water line (20ft below) or power lines above. What type of berm or 1-2' high divider would be best to keep water? Brick, block, wood? And Thanks for input on rail ties, leaching creosote makes sense!)

I'm by no means an expert on the subject, but from what I can see you need to bring in top soil and build up your property - level to the same as his so his water doesn't flow down onto yours. Then add new sod to the top. Or you could do stones the same as his. Even if he put 2 downspouts on the eaves the water would still run down to your property as you are "down hill" to his.

So when a property's site plan is approved, one of the things they look at is where the water (theoretically, anyhow) will go as it moves from property to property. Generally speaking, if there's nowhere to go from where you are, the city/county/village will either put in a drain to the storm sewer, or mandate infiltration trenches, etc. Since you don't have that I'm assuming there's somewhere downhill from you that water can go?

@Angel - story time! My house sits at the top of the street. My rear property line, which is 90 feet behind me, is +/- 93" lower than my first floor elevation. There's a rental house maybe 8 ft beyond my property line, then the hill goes back up on the other side of them. They're pretty screwed, so the town has a storm drain at the street at the low point.

In 2014 we had a crazy storm, something like 12" of rain in one weekend. It actually collapsed their basement, the house was condemned till it was fixed. After fixing the basement their contractor regraded and built the soil up. Next moderate rain storm I had 6-9" of standing water in my backyard! I called the town engineer and raised hell, he came out, the property management company got called on the carpet, and they had to fix what they did. Had they not, I would have had a case for damages. I was happy to advise how to deal with their water issues gratis, even though the property management company is the devil incarnate, but I'm not cool with suddenly owning 10 feet of swampland.

Even though a chunk of the stormwater comes down my yard, they were preventing it from reaching the storm drain. That's not allowed. That's why I'm saying that the OP needs to be super careful what they do, and involving a local pro is prudent. Raising the grade up on the OP's property could be problematic if it results in the neighbor suddenly having water pooling around the garage.

What's in front of your house? Could you direct the water down the side of your house out to the street?

My front downspouts run down the walk to the street so I suppose drain from back to front could work if it was sloped correctly. Id probably need professional help with something like that.

I think your right, a pro is needed. No amount of advice on here will substitute for a professional evaluation of the property.

Could you do a trough with a rain garden? That would collect the water and look attractive if done well.