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Your mother (and in all liklihood your father too) are going to be pretty emotional, irritable, and short-tempered because of the stress of this. They are bound to act irrationally. Right now, I suspect you are just going to have to try not to react when she has a go at you, and put up with it.
They'll need you to be for them, and they need to know you still love them. If your mother us saying that it's none of your business, you may be best off not talking too much about their relationship and breakup, but focussing on being for there and helping her cope with life in a city that she's not familiar with.
While it may be tempting to try and help out with their breakup situation, and will be done no doubt with the best of intentions, the reality is that nothing you say or do is likely to make much difference to the outcome. The only people who can really affect that are your parents themselves. However, you could do damage to your relationship with either or both of them if they feel you are interfering, or, worse they feel you are taking sides at all (even if you aren't).
Try to be tolerant, forgiving, helpful and supporting while they go through this tough time. It won't be easy.
But, don't forget about yourself and your own "peace of mind." It's real easy to get sucked into such problems and become stressed-out and overwhelmed. Be supportive of your parents; be careful about "choosing sides." And, don't neglect yourself and your own need of mental "space."
Good luck!