"End of tether" ..... after a month, when, according to the OP, there has been one incident of shitting, one incident of peeing, a broken bit of crockery (accident), one bite and one swipe.
TBH ..... if that's the full story, then if that's all the cat's done in the first month since moving into a new home, which also has another cat in it who keeps going for her, then the OP's got off lightly. Those sorts of things are to be expected and whilst obviously unpleasant, are within the realms of normal when introducing and settling a new cat in. You're also being very unrealistic if you expect cats never to swipe if there are kids about scaring/teasing it.
It's clear however, as others have said, that the OP doesn't have the patience to seek out solutions for this .... for example, by coming onto MN and asking for advice along the lines of "new cat problems" and/or checking there are no underlying medical problems with the vet. Instead, her immediate reaction is fury and a ridiculous assertion that this frightened animal is being deliberately bad. Thankfully her first cat must be a model creature, but every animal is an individual and it's plainly ridiculous to expect them to all be instantly trouble free.
Having said all that, I'm not advocating for a minute that the OP perseveres .... some people simply aren't cut out to be pet owners, though regretably many of those who fall into that category are. They're fine while everything's running smoothly but regard the animal as something disposable when they become hard work, e.g. through illness, accident or some sort of upset. Just hope she does the right thing but I don't think people are being too harsh. I wonder what she expected when introducing a new pet into a home where there was already a resident ? It can be done (I've done it many times in a so called multi cat household), but you also need to be realistic about the space available, easy access to hiding places, free access to ample outside space, multi food stations and litter trays etc as well as taking very careful note of the personalities concerned. If in any doubt don't, and even if you're hopeful it'll work, be prepared to rehome responsibly if it doesn't.