One company already refused to sign anything, and what do I do if they don't sign the NDA and they decide to just go ahead and use the invention. I don't have a patent yet. What would be my recourse.
You don't have any recourse in this case. If you had a patent issued, you could sue them for patent infringement. If you had an NDA is place, you could sue for breach of contract or misappropriation of a trade secret. If you have neither, you have no standing to sue for anything, because you don't have anything.
A provisional patent is nothing -- it's sole purpose is to allow an inventor to establish an early "priority date" -- a filing date -- while giving said inventor some time (1 year) to get the full patent application together. Nothing more, nothing less.
Even if you had a nonprovisional application in the works, you still don't have anything you can enforce until the patent actually issues.
Currently, all you have is a trade secret. Now, trade secrets can be protected, but you have to keep them secret in order to protect them. If you tell someone else, they are no longer secrets, unless you have an NDA in place.
All that said, if you go ahead and talk with these companies with your provisional, and they steal it, you can still go ahead, turn your provisional into a nonprovisional, and then once your patent issues, sue them for infringement. Since the priority date of the provisional would be before they saw it, there would be no "prior use" or "prior invention" problems that would keep you from obtaining a patent.
Just for completeness, the reason why the companies don't want to sign an NDA is probably one of two reasons -- first, your NDA may be overly burdensome on them, and second (and more likely), they have no way to know whether or not a patent will ever issue on your product, and they don't want to have the NDA hanging over their head if the invention doesn't get a patent and it starts to get used. If the NDA were there, potentially you could take your invention and sell it to someone else, and the company with whom you signed an NDA would be unable to compete without facing a potential breach of contract action.
You need to decide what you want to do -- either risk having your invention stolen without an NDA, or wait until you've got a patent (or are at least far enough down the patent application road to be somewhat assured that the patent will issue).
