Strengthen the military in the short term
Your military will be able to produce more tanks, weapons, fighter jets, and defense systems than it normally would have. If Russia were to invade, they would still be able to win a conflict because they have one of the best militaries in the world, but your military will be strong enough to both lengthen the war and raise the costs of war. Even if the communist bloc was weakened, the military buildup may deter the Russians from invading. This military buildup would come at the opportunity cost of investing in your developing domestic industries.
You have chosen a pure economic liberalist approach to developing your economy. Your infant domestic industries are fully open to both domestic and international competition. Fortunately, your economy will benefit from your international economic relations through absolute gains and access to more markets and resources. If your industries do not lose out to global competition, then, over time, your industries will innovate and develop to the point where they also make relative gains in an open world economy. Furthermore, your membership to all of those institutions increased your linkages with the capitalist bloc. The US has fully committed to a security agreement with Chechnya.
Your choice to reject the Russian offers and reallocate resources to your military has resulted in a moderate strengthening of your military. However, your developing industries have not grown much because you stripped them of their excess resources.
Recently, two states succumbed to the capitalist bloc's pressure and switched from communist economic systems to capitalist economic systems. This has emboldened Russia. Still, Russia has no economic leverage over Chechnya because you decided not to become economically dependent upon them. You have also made the Russian decision to invade Chechnya more difficult because your strengthened military has raised the costs of war.
The Russians decide not to invade Chechnya because your security guarantee with the American bloc and modernized military have raised the costs of war too high. Congratulations, you have successfully maneuvered through a potential crisis despite having to make some tough decisions between economic and military investment.