Buddhist take on parents staying together for the children? 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.