We rehomed a cat from Cats Protection a few years ago. She came to us supposedly house trained, but wasn't. We're no stranger to rehoming cats, but despite trying everything she was never house trained - we'd find shit everywhere...kitchen surfaces, sofas, behind doors, you name it, we found cat shit there. One that sticks in my mind was was having to clear it off DDs bed.
We went to the vets, tried diffusers, litter trays in every room, keeping her in one room, and so on. After two years of this, we finally admitted defeat and took her to an animal sanctuary.
Prior to this, I had asked for advice on another forum - can't remember which now (I've wiped it from my memory) - and I was royally flamed for not sticking with it and trying to sort things out.
But two sodding years of clearing up cat shit really was enough.
OP, you have to do what you think is best, you really do - if you've had enough, then it's time to take her back. I see your situation is slightly different to mine, in that your cat has only recently started, but if there is no sign that things can get better, then you have to make the decision about what to do for the best. It's a highly emotive subject, but you have to do what's right for you and your family.