You paint a vivid picture of an absolute political mess, one that the wisdom of Solomon cannot sort out. So, I guess my vote would be to stay out and not try to have WWIII in a place that is only slightly less strategically isolated than outer Mongolia.
Unfortunately the world does matter and we have to address it.
"On February 2, the US and Georgia signed an agreement to fight nuclear smuggling by providing assistance for border surveillance, enhancing ties with the international community on nuclear forensics and reinforcing the work of the Georgian Nuclear Regulation Agency. The first American delegation to come to Georgia to explore ways of improving the countrys defenses against nuclear smuggling arrived in mid-September 2006."