This is an html issue. Unfortunately, what you want to do is contrary to standard browser/form/html behavior, so any solution will be some sort of hack. A reload button or link is the cleanest, easiest solution, but doesn't allow the user to use the reload button on his/her browser. Allowing the form to be resubmitted (and ignoring it) is a bad idea - it will be confusing to your users, whose browsers will ask (every time) if they really want to resubmit the information (plus, it's a lot of work). Redirecting after the form submission is also bad because it hoses the back button (although you might be able to change the behavior of the back button with javascript - you could probably get some inspiration from porn popups on how to do that). Plently of websites hose the back button in this way, but that doesn't make it less of a sin.
There is a horrible hack to do exactly what you want, but it involves frames (iframes might work) and javascript. Basically, you have to subvert the standard form submission process - instead of having your form's submit button actually submit the form, have it set off some javascript (using onClick) in another frame (iframe?) - we'll call that frameB - that submits a form (from frameB) with the information from the original frame (frameA - the one with the form the user filled out). When frameB comes back from the server, it reloads frameA using javascript (you may have to shift focus back to the original window, again with javascript). The back button works - the reload button works - and there is no annoying "are you sure you want to resubmit the form" warning message. Since you are coding an application, frames are not a Bad Thing.
If you don't have frames in the application already, I'd just do the reload button/link (although you could see if the javascript/frames thing works with iframes - I can't see why it wouldn't)...
redirecting only breaks the browsers back button when you use a meta or javascript redirect on the html page. when using a http-header redirect there will be only one page in the browsers history.