mindgarden saidPruning one root won't hurt a tree. Depending on the person involved, bringing in the neighbor could just cause bad craziness. If you go with chemical warfare, don't use a systemic herbicide - that would go back up the root and kill the whole tree. If you have trees near the house, it's kind of hard to keep roots out of the foundation drains, unless you spike them with something like copper sulfate once in a while. That won't hurt the rest of the tree.
I've planted a crap load of stuff and when I come across a root an inch or more I try to plant around it instead of cutting so it hurts me to cut this one but I can't let it hurt the house so I gotta saw snip that.
I like to be as upfront as I can but I see your point with the neighbor. I think she'd be okay and in fact she'd probably be more concerned with her tree damaging my house but maybe as you say best to not say.
No way will I use chemicals. It's a nice tree. I hope to not damage it. I'll dig that side of my house and see if I can't get it back at least three or five feet from the foundation and then reinspect every 10 years & recut as required.
We don't have foundation drainage issues in most if not all of Florida as the soil here generally is sandy and drains readily. My last house was built on an old dune and wouldn't even flood in a hurricane with all the water those things drop. Here I'm at a higher elevation with very deep sand. Though this property slopes slightly, so I get some water in a big rain at the lower end but within 10 minutes of even our major Florida downpours it drains dry. The bamboo is very happy to be growing here.