Anything I can do with my cat and neighbours?

Ever since we've had her we have had issues with neighbours interfering to her detriment. At the beginning the neighbourhood basically assumed she was too young to be outside (which she wasn't, we followed our vets advice exactly).

So they began feeding her, now the problem is they were feeding her supermarket basic food and we were feeding her more expensive stuff, my understanding is that the basic stuff is like us eating a takeaway vs a nutritional meal, cats may enjoy it but it isnt nutritionally as good.

This lead to her stopping eating the food at home, and us going through a faff trying to replace it with something shed actually eat. Then we had neighbours come round shouting at us for their dog nearly killing her when she comes around, but shes only there because shes been fed for no reason other than they decided she was still a baby because shes small.

She was seeing the vet regularly and weighed completely fine, so its not as if she was even starving for them to begin feeding her yknow?

She is extremely friendly and I think this is why people want her. They ended up taking her and basically acting like it was their cat. They put a collar on her and changed her name (and kept her indoors). We eventually got her back where they made some half hearted excuse about posting on Facebook. I had also done this. Plus shes chipped?

Anyway fast forward we kept her inside for a long time and she was great. Other than the difficulty of keeping her indoors when she so clearly wanted out. We let her out and we noticed the same thing again, she was refusing her food. She then over 2 days vomited up cat food after coming home but it wasn't hers as hers remained untouched. She also must have felt poorly from it because she was extremely clingy over these days and refused to eat anything.

Then a boy from the family that took her knocked on my door asking if it was my cat. I said yes, he said she looks like she hasn't eaten in days. I said thats not really correct because someone has been feeding her as shes throwing it up (knowing it was likely them).

He then said hed only fed her once some biscuits, I said no, shes throwing up pouches. He then called her over using her name, so he clearly knew exactly what cat it was and where it lived.

He then tried to say she doesnt like being picked up and I had to bite my tongue and not say, yeah by you maybe. Cause she is in my arms 90% of the time.

Its honestly doing my head in. I feel like the options are keep her indoors or move at this point. But it isnt fair on her and really the logistics of moving are crazy just because some family thinks theyre entitled to my cat. Any advice?