Before answering the actual question, let's have a look at pushing and pulling on rules:
The verb »schieben« means to apply physical force on a thing to move it in a sliding manner over the ground. But a rule is not something physical. You can't touch a rule and especially you can't change the location of a rule because rules usually don't have such a fixed location. I think what you mean is changing a rule. So in a figurative sense you don't want to move the unchanged rule to another place, but you want to change its shape and leave it where it is now. For changing the shape there are many German verbs, in this case the pair »zupfen« and »zerren« fits very well. Even better are »herumzupfen« and »herumzerren«:
- zupfen: to twitch at something, to pluck, to pick
»Zupfen« means: you grab a tiny extension of a bigger thing with your fingertips, pull on it and then release it (often used when playing string instruments in the pizzicato mode, but also hairstylists do it with their customers hair). The aim of »zupfen« is never to move the big thing.
- herumzupfen: zupfen without having a plan. You do it because you are bored (on your clothes for example) of just to see to what it may lead.
- zerren: to tug, to wrench, to jerk, to twitch
Very similar to zupfen, but you grab big parts of the bigger thing and pull with both hands on it. The aim of »zerren« is often to move the big thing, but not necessary. »Zerren« often doesn't move the object. (But »schieben« by definition describes the movement of the pushed object.)
- herumzerren: zerren without having a plan.
So, I would say it this way:
Wir können an den Regeln 2 und 3 herumzupfen und -zerren, aber wir werden damit nirgendwohin kommen.
We can pick and tug at rules 2 and 3, but we're not going to get anywhere with it.
Answer to the actual question
First of all you should be aware, that the verb »kommen« (to come) can also mean to have an orgasm, while »hinkommen« (to come to a place) never can have this meaning. And this is why this is the correct translation:
Wir können nirgendwo kommen.
We can't have an orgasm anywhere.
The adverb »nirgendwo« is a local adverb, so grammatically it stands for a place or a location. It definitely does not stand for a movement. But kommen (if not meant in a sexual way) always needs a context of movement:
Alice: »Ich bin im Supermarkt. Kannst du bitte zu mir kommen?«
Bob: »Ja, ich komme gleich.«
Here both people are talking about Bob moving towards the supermarket. So we have a movement and we can use kommen.
But when the context explicitly provides a location that is not the target of a movement, then any verb describes an action, that happens at this place, without leaving this place and without entering this place.
Georg geht in der Küche.
Georg walks inside the kitchen.
Here the context clearly provides a place (this happens by using the dative case), so gehen can only happen inside this place. Georg doesn't enter the kitchen and he doesn't leave it. He walks in circles inside the kitchen.
Georg kommt in der Küche.
Here we have the very same context: Here it is the dative case, that defines, that the action happens on/at/in a place; in your example it was a local adverb (nirgendwo). But the effect is the same: It means that Georg doesn't enter the kitchen and he doesn't leave it. And the only way to interpret the verb »kommen« in a non-directional context is, that Georg has an orgasm in the kitchen.
Georg kommt nirgendwo.
Here the prepositional object with dative case is replaced with the local adverb of your example. I already explained what this means: Georg does not have an orgasm anywhere. The last part of your sentence (Wir können nirgendwo kommen) is just a variation on this theme.
What can you do?
Use another verb instead of »kommen« (to come). The best choice is »hinkommen« (to get to a place). It is a separable verb, which means, that the prefix hin can be separated from the verb in some grammatical situations and then stands at the end of the sentence:
Ich werde morgen hinkommen.
I will get there tomorrow.
Ich komme morgen hin.
I will get there tomorrow.
So, you can say:
Wir können nirgendwo hinkommen.
We can get nowhere. (We have nowhere to go.)
About your examples from DWDS
These examples use different patterns:
es kommt zu etwas
jemand kommt in eine Tätigkeit
someone gets into an action
These phrases use the verb kommen, but not in a local sense. It uses it in a modal sense. Here are the correct translations of your examples:
Zu einer Abkühlung oder einem Anstieg des pH-Wertes wird es den Prognosen zufolge nirgendwo kommen.
Cooling or increase in pH is not projected to occur anywhere.
In dieser Mischung aus literarischem Roadmovie und Gaunerkomödie hat jedes kleine Detail seinen Sinn, nirgendwo kommt der Erzähler ins Schwafeln, nichts ist überflüssig.
In this mixture of literary road movie and rogue comedy, every little detail makes sense, nowhere does the narrator get into rambling, nothing is superfluous.