Imagine the following situation. Somebody is doing their PhD in field A in the US. Suppose they became interested in a different field, field B, and consider doing PhD in field B instead. Suppose further that the university they are doing PhD at is not suitable for doing PhD in field B for some reason. Is it acceptable to apply for PhD positions in field B in other universities without notifying their current university until after they have been admitted to a program of their interest? The reason for doing this is to ensure that if they don't get accepted anywhere, then they could just continue pursuing their PhD in field A (which is also an acceptable option for them).
In most fields in the US this would be acceptable. An exception might be if you have accepted a grant that has some sort of termination clause that prevents it or makes it difficult. If you wind up leaving your current position you might have some ethical obligation to finish up some tasks if they affect others, but that is a separate question.
In general, though, you can seek a better position for yourself.
But you will also need to be able to explain to the new institution why you are leaving and why you are a good prospect for their program. Self awareness and learning are usually a good reason that (most) people will accept.
I believe that what you're trying to do is feasible and sensible, but just make sure that you really want to pursue the PhD in the field B, otherwise while being on the field B you might get interested on a field C, that is also quite common and could become a vicious cycle. So just be sure about it and good luck with your applications!
I believe that it may be next to impossible to not let anyone in your current program know of your plans. Unless all of your previous letter writers are still available to write you letters of recommendation for a new application, you will likely need to find someone at your current university to write you a letter.
If you have an advisor, I would work with him or her to prepare a plan for applying to different programs. I would be upfront and direct about the fact that you want to switch disciplines. You do have the right to pursue disciplines you are most interested in. Being sneaky about your plans could result in trouble.
As with any graduate admissions situation, you will also need to be prepared to provide a compelling reason to the new PhD program as to why you feel you should be admitted to their program. This can be increasingly difficult to do when you have already been enrolled in another PhD program. It usually is not sufficient to just say
"I really love botany (or whatever subject you want to enroll in). It is really interesting to me."
I see some variant of that statement in a large number of applications, and it is never compelling. Such verbiage is especially common in applications of students who are switching disciplines. While being interested in a subject is necessary, it is not sufficient for admission into a PhD program. This is not to say that switching disciplines is bad (I did it myself). It just means that you cannot rely on "interest" alone in getting you into a PhD program. (I'm interested in art. But I know nothing formal [academically speaking] about art. It could be hard to convince an admissions committee that I'm a great choice for their art history program).