I think I would also be inclined at this stage with all your best efforts to terminate. There isn't just one issue here for you to deal with. If not, then I would be inclined to give only 2 weeks notice not 4 for probation and at the end of the two weeks if you see no improvement in the childs behaviour then her spot will be terminated. This 2 weeks probation will be her notice period so no, I wouldn't give an additional 1 week after that.

There was another post last week addressing a child who was much younger, 22mths I think, who was physical with the other children. I would take a similar approach and even though this child is 3.5, I would strap them in a highchair in an area away from the kids but where you can still see her. Another option would be to separate a portion of the room off and tell her that if she can not play appropriately then she plays in that space alone until she learns. Every single time there is an incident she goes in there. Not quite like a time out with 1 minute for every year, but an extended period of time to teach her that this is how she will spend her DAY if she does not play appropriately. When the other children are in your living area she gets strapped in a highchair and told that she can not be trusted to not pull things apart so she has to stay there until she earns your trust back. She will soon learn. The same at pick up time. Explain to her just before pick up today that if she is defiant and runs all over the place and misbehaves then tomorrow you will dress her and put her in a highchair to wait for mum. If her mum doesn't like this then ask her what she suggests they do instead to change things as you have brought it up with her before and she hasn't followed through on any of your requests and without consequences her child has no incentive to behave.

As for potty training, surely at her age she should have some regularity with her BM's by now?? I know this isn't 100% for any child but generally speaking you know when a child is going to poop. I think once you have the behaviour under control then the toilet training will no longer be as big an issue. She will likely be more cooperative and be more responsive to positive reinforcement.

My whole perspective on potty training differs from most on here so this is just my opinion, but the pull up being on this child for an extended period of time is also part of the problem I think. It is a diaper, she knows it is a diaper, and she knows she can pee and poop in it. Either put her in underwear except for naptimes, which I'm thinking isn't an option if she is peeing and pooping all over the place all the time, or put her back in real diapers and stop training her. Do one thing at a time and take the focus off the fact that she is not trained and all her accidents, or purposeful doodling in her pants.