As a manager, you absolutely cannot bring your personal problems to work with you. Plain and simple.
There have been times where stress has gotten the better all of us. It's important to learn the triggers that cause this stress and also learn how to recognize when you may not be at your best. By knowing when your judgement is affected by stress, you can make adjustments to your own behavior.
For example, I personally try not to criticize anyone while I'm under duress, as I know I'm more likely to overreact. Instead, I either get the opinion of a third party beforehand, or I wait until the stress is not so high and when I know I can be objective.
With that said, there are times when stress does occasionally get the better of us and we say or do things we wouldn't otherwise do under normal circumstances. If that does happen, be an adult and apologize. As long as you aren't making a habit of blowing up on people, most people will understand that you too are human, like they are, and you will be forgiven.
Since the success of a manager is defined by the ability to provide motivation and leadership and earning the respect of others, broken relationships will never help you reach your goals. You can't lead and motivate people who don't respect you as a leader. In summary, at no point in time is a broken relationship acceptable.
I find Rudyard Kipling's poem, "If" to be a great source of inspiration. When all those about you are losing their head, this is when you must keep yours.