This what I have said to her but she is saying because she has paid for it it’s up to her to do what she wants but we both share the same downpipe so surely she can’t restrict mine from flowing mine is the white gutter you can see how they have attached mine back to hers but it goes up
We had new half round installed on our semi, with a shared downpipes, front and back, down the middle. After a few years, without consulting us - next door had a cowboy, fit new square, fascias and soffits, joining our half round to the new square, but without proper adaptors, and as you would expect, it flooded down our outside wall. Despite strong words, they wouldn't sort it out.
I ended up resolving it, by fitting new fascias, soffits, and our would seem to have the downpipe, meaning the only way you can get your side to flow, would be to either lower her gutter system, or raise the level your own. You could also write a formal letter, inviting her to get a proper tradesman in to rectify it, or threaten legal action if it is not resolved.
Other than that, you could sabotage it, by blocking the end of her gutter, where it joins, and ensure your own gutters is able to drain and flow down her wall.