第一句：We are sorry to bring you so much trouble.

A:We are sorry to bring you so much trouble.
我们很抱歉给贵方带来了这么大的麻烦。
B:We hope that this dispute can be settled through friendly negotiation without ite being submitted for arbitration.
我们希望争议能够经过友好协商得以解决而不必送交仲裁。
A:Yes. That's what we want.
是的，这也是我们所期望的。

第二句：I promise it will not happen again.

A:We hope that threre will be no repetition of this kind of trouble in the future.
我们希望这种问题今后不会发生了。
B:Yes. I promise it will not happen again.
是的。我保证这种事以后不会再发生了。
A:We look forward to your settlement at an early date.
我们期盼你们早日解决此事。
B:We will inform you as soon as possible.
我们会尽快通知贵方的。

知识点延伸：

如果错误在己方，应该先向对方表示抱歉，尽量不要诉诸于法律或是仲裁。并保证下次会更加小心，不会发生类似的事件，还要尽快通知对方处理的情况。

1.其他表达法：

We are looking forward to having your early reply to this matter.
我们期待你们尽早解决此事。

Your early settlement of this case will be appreciated.
如果你方能尽早解决此事，我方将十分感激。

2.as soon as possible 尽快

We also had to refine the schedule and get our exploratory phase underway as soon as possible.
我们也必须细化我们的时间进度表，并尽快的开始我们探测好的起步阶段。

I recommend that psychiatrists should try to offer [patients] as much participation as soon as possible.
所以，我建议医生们应该尽快的让病人多参与到治疗的过程中来。