I am curious what other folks think about this, but here is my take:
Based on the question that this is linked to about a cheating spouse, I suspect that there is a lot more emotional baggage to any particulars than I am going to address here.
You ask if breaking the cycle of exclusivist/monogamous marriage means divorce. Maybe, if that seems appropriate to both (or either party) establishing the autonomy they need. Maybe not, if there are reasons to stay together and the economic/social benefits of doing so (or, conversely, the inconvenience or negative baggage of going through with divorce) are more heavily weighted. If you're already married then there are some material benefits to remaining so, and renouncing the legal sanction of such seems irrelevant or, at best, symbolic, unless of course, this relationship is not working anymore at all, in any way, in which case it is in one or both parties best interest to get out of the legal contract now.
As to the more anarchist part of my response to this: what might you do instead of divorce? Talk? Figure out what your individual needs and desires are, and how you can help each other meet some (or all) of them. Or not. Do you need/desire other partners? talk about what each of your capacities are for that. If you find you still have enough common ground and affinity to maintain a relationship, great. If not, good on you for recognizing it and moving forth as individuals.
As to the more loaded question (whether it is authoritarian to investigate suspected dishonesty in personal relationships): No, it isn't authoritarian, per se, but it is worth exploring why exactly it matters, and why asking as opposed to investigating isn't an acceptable option. In terms or a romantic relationship the need to investigate whether or not the partner has been "cheating" (in quotes because that means different things in different situations, and if you weren't clear on what it meant at the outset, potentially in a particular relationship to different individuals), that raises some red flags for me. Particularly I think ideas of ownership of another person's love or affection need to be examined.