One of the things I tried to put across in Watching the Clock is that the DTI's ability to regulate time travel is extremely limited in practice. After all, it has no jurisdiction over other nations, no way of controlling temporal research going on in distant parts of the galaxy that haven't been contacted yet, and no way of restricting temporal intervention by people from the future (or advanced alien civilizations from the past). They do what little they can to identify and minimize known risks, but the sheer hopelessness of gaining any real control is one of the things that makes the job so stressful.
When feasible, as I showed in WTC, the DTI coordinates with other governments' temporal regulation agencies, or negotiates with their governments to try to convince them to embrace a responsible approach toward time travel (as with Ranjea & Garcia's negotiations re: the Axis of Time). But all they can do is advise, cajole, and seek cooperation. They aren't an army, just a bunch of bureaucrats and investigators. So no, they don't have the right to invade a sovereign nation and steal their time machines.
Temporal research within the UFP is subject to the laws that were put in place in 2270 (read Forgotten History for more on that). Of course, theoretical research is freely permitted, but practical experimentation is subject to regulation on safety grounds, the same way that the US government regulates nuclear energy and other potentially hazardous pursuits. (By analogy, the information about how to build a nuclear bomb can easily be obtained from the library or the Internet, since it's basic physics and engineering, but it would be illegal to build a bomb or possess nuclear material without the proper government licenses, and those wouldn't be easy to come by.) The DTI would function as the regulatory agency responsible for enforcing the laws. They'd crack down on any unlicensed temporal experimentation and supervise any licensed experimentation.
Possession of a temporal artifact such as the Orb of Time would probably be something that would require a federal license, but it wouldn't automatically be prohibited, just regulated. If possession of such an artifact could be justified, then a license could be granted. Given that the OoT was in Bajoran possession for thousands of years without any evident damage to the timeline, and given its importance as a religious artifact, I'd think the Federation would be willing to recognize the Vedek Assembly's right to possess the artifact. But actually using it for time travel would probably be subject to Federation laws and be rather more restricted (in the same way that it can be legal to own a firearm but illegal to discharge it except in specific places and circumstances).