It's pretty standard that if East Germany invaded, NATO responds, Soviet forces support them.
This I very much doubt. The OP states that East Germany attemps an attack on West Germany. Not that Moscow or the Warsaw Pact does so. So there must be a rift between those East Germans who want to start this attack and Moscow in the scenario proposed. But I can only imagine something like this attempted by a group of East German conspirators. Loose canons who (for whatever reason) believe kicking off an incident at the inner German border is something in their interest. Rather deluded interests I would gather.
If some conspiratory group like that in the East German puppet government or East German vassal military starts to plot to incite a war with West Germany (and by extension NATO) the USSR puts down its mighty foot right when it gets wind of this and tells whoever is behind this idea to stop this nonsense. Probably before any troops are even mobilized for such a move or before they reach the border. The higher up in the hierarchy the conspirators are, the more likely and earlier it gets exposed. How the conspirators will be dealt with depends when this happens, who is behind it and for what reasons. None of which may come to light ever and the whole conspiracy hushed up and lost to history.
But lets say these East German conspirators actually do manage to send units into a forray and clashes across the German-German border without alerting their masters in Moscow before it is too late. It will most likely be only rather small units and as such only be able to create an 'incident' - nothing big enough for a proper invasion. But as said above: These conspirators may think an incident is all they need for their aims. Or they overestimate how far they can get with what they have. But with what little they have at hand, they may not even make it past the NATO trip wire units across the border. The lower they are in the East German hierarchy, the less they will have at hand.
Question then is: How does Moscow react to this incident? Not to mention NATO? This is a very volatile scenario in a very volatile area and era. But I do not think nukes will fly right away. My best bet is: Everyone gets away with a mighty scare before this conspiracy fails. How big a scare depends on how big the units are these conspirators can manage to get to the border - a platoon, a regiment, a company - if they even get this far and not get intercepted by other Warsaw Pact forces before (see further up above).
Afterwards the instigators of this incident will be rounded up by the KGB, probably with further purges and witch hunts of the East German government. Warsaw Pact units not stepping to the tune of Moscow is something that can not be tollerated by Moscow. Then the blame game between the US and USSR starts who's fault this all was.
Overall though I think the probablity for nuclear war is rather low in this scenario. Except if NATO is extremely trigger happy - which I also do not see. But the tail (East Germany) will not be able to wag the dog (Moscow) into a nuclear exchange over ... what exactly did these East Germans actually hope to achieve?