Yep, Julie is right: She is perfectly well aware of your intense stress over this and is reflecting it with her own stress and desire for control. Nothing is wrong with her. She is being three, and exertiing her independence because she knows for certain that you cannot MAKE her do anything in a potty.
You don't want to hear this part but here it goes: There are three things we adults cannot force a child to do: Eat. Sleep. Use the potty. THEY must control these things -- or we must let them think they do.
You say she is in OT for both sensory and behavioral issues. That's a red flag to me -- isn't it one for you? She may be feeling that she's already told what to do in OT and isn't about to let another adult (you) tell her what to do about something she has figured out she can control (pottying).
Have you discussed this with her OT therapist at all? I would definitely involve the therapist. Probably the therapist, if it's someone who has worked with this age group a lot, will be able to give you an opinion on whether this is a bad time to be so focused on potty training and whether you should let this go for a while longer. If your daughter is working hard in OT right now it may not be the time to push potty training. You will not scar her for life if you leave it and come back to it in a month or two.
It sounds as if the school she will attend and their potty training requirement are making you very, very stressed about this. Having a deadline for potty training is more often a problem than a motivator, I've found. The harder the parent pushes, the harder the child resists, especially a child like yours whose currency is hard to find and who has other issues to handle. Is the school aware that she has these sensory and behavioral issues and that she is receiving OT? Is it a "throw the child out if she doesn't use the potty 100 percent of the time" school? Or do they have some understanding that individual kids will have accidents? I would ensure that they know now, not later, that you are working on this but that she also has other issues that may mean she is not perfectly trained by September.
I know you say that "every single child I know her age are all potty trained, yes, every one of them." But unless you're with those families 24/7, you don't know that these kids who are perfectly "trained" all day wet the bed all night long, or fight their parents like crazy when at home. Please don't let your idea that your child is somehow behind her peers influence you like this -- it is another factor adding to your stress. You also ask "What is the latest she will achieve this" as if there is a magic age when all kids are definitely trained. You know that's not the case.
I've seldom seen a post on here quite this stressed about potty training. Are there other stresses in your life and hers right now? Is there some feeliing that "if she doesn't go to this school it's all over for us"? You describe her as "tough" -- is she very resistant and defiant about everything else, not just potty training? In other words, is there a lot more going on here and potty training is currently the form that the battle between you two is taking? Some help might be in order if that's the case. Again, how much does the OT talk with you about her behavior and what you can do at home to work on it outside OT sessions? Do you get any breaks from your tough child? If not, can you get some?