How would one go about figuring out if it is wise to stay together for the sake of the children or if it is time to split up?
What would be the guiding principles for figuring this out based on Buddhist principles and Buddha's advice for married couples and the general sentiment of the teachings historically attributed to the Buddha.
Prefer answers based on Vibhajavadin traditions and texts held to be true by those schools.
What would be the guiding principles for figuring this out based on Buddhist principles and Buddha's advice for married couples and the general sentiment of the teachings historically attributed to the Buddha.
As others already mentioned, the teaching is mostly for monastics with some small portion just giving generic advice to the lays. However, one can always use logic and common sense to come up with the best solution for everyone. A common mistake is the automatic assumption about the benefit of sacrificing oneself for the sake of the children, while in reality, there're instances where it's even more harmful to them. Imagine staying with your spouse, but engaging in constant back and forth arguments using harsh, abusive language, Or, on the other extreme, remain completely silent and let the spouse spewing all the nasty words all day long. Both of those stay-together scenarios would actually do more harm to the children than good. So, use one's own intelligence and common sense to evaluate the situation. While it'd obviously be best for parents to try to work things out and stay together, but if that means it'll create a living hell for both parties, and/or it doesn't actually benefit children, or even does more harm to them, then one might have to consider the idea to go one's own separate way, for the sake of everyone involved.
The suttas are mostly (not all) by and for monks, less detailed on the subject of married life and so on.
Buddhism & Divorce implies there's not a lot of explicit doctrine on the subject -- perhaps little more than that "lay life is confining and a dusty path".
You might be interested in a book The Buddha's Teachings to Laypeople: Practical Advice for Prosperity and Lasting Happiness. from which I summarised this answer -- it's based on the author's finding suttas that are relevant to lay life -- unfortunately I don't own a copy so I can't tell you now what it says about children.
This article -- A Happy Married Life -- might be helpful. It includes a section "Parental Responsibilities" (I'd suggest you read first only the first sentence of each paragraph to get an overview).
Again I imagine that the situations vary and that you could use some proper (personal, in-person and perhaps professional) counsel. When I tried to answer your question What's the advice for dealing with an abusive partner? I did so without considering that there might be children involved, in the house. In my limited personal experience I think that children are better with one parent who loves them than with two who don't, and personally I always imagined that if I were a parent myself then I might be less willing and less able (because it would be less moral, less dutiful) to tolerate (condone, perpetuate) an abusive or less-than-ideal partner, even or especially "for the children". But this is me describing or generalising from my personal experience, not yours -- so for that and other reasons I suggest you find a counsellor to discuss this with. Like if you were ill you should probably talk with a doctor in person, not self-diagnose nor read a book of pharmacology.
