Hi, Helen. I understand how upsetting this can be.
In today's copy/paste era, if your tree is public, this type of thing is bound to happen. If you've shared any genealogy with anyone anywhere in any way, whether on paper through the mail or via email, etc., there's an extremely high likelihood that you will see it in an online tree.
I don't have a public tree but every well-researched (and self-funded) family tree that I have shared with cousins has been posted online to their own trees without them asking permission, with the rare exception of one distant cousin who has put my data into her private tree (with my knowledge).
Here's something that happened to me. My brother and I did our DNA tests and I uploaded an extremely basic, short tree to Ancestry for both of us. It was public for a short time. In that time, someone sent a PM to my brother because they have a very distant cousin match. (We're in Canada, this man is in the US.) I responded, because although this man and I don't have a match, I'm managing my brother's DNA results.
This man could only see my public, very basic tree, and I didn't name my parents, so I thought my privacy would be preserved. Unfortunately, due to my other cousins uploading my research, and then many other people copying and pasting it into their trees, this man in the US was able to connect their trees with my grandparents. He informed me (correctly) that he had figured out that my father was one of the two sons of so-and-so. This upset me a great deal and I promptly made my basic tree private.
This man is guessing that we are related through one particular family line, although he hasn't been able to research our families that far back (and neither have I). This would make him a distant relative through my mother. Over time, this man has copied and pasted both my mother's and my father's extensive lines (including every side branch he can find) from various copy/pasters on Ancestry. Why he feels a need to add my father's family to his tree, I have no idea. He has labelled everything to do with my family with my brother's initials. He has no idea how we're related but he seems to be intent on hoovering up every relative of mine that he can find.
This is how people end up with 60,000 people in their online trees.
I've come to the realization that, if I don't want something proliferating all over the internet with no credit or thanks to me, and with no way for serious researchers to contact me, I can't share it with anyone. It's a real conundrum for me and I still haven't figured out how to feel good about the situation with the online free-for-all copy/paste brigade. I hope you are able to sort it out for yourself and feel better soon.