Final answer:
Lady Semore apologizes for the complicated emotions and troubles that her actions have indirectly caused to others, reflecting the intricate nature of human relationships.
Step-by-step explanation:
Lady Semore in the provided extracts apologizes because she's experiencing a mixture of regret, guilt, and recognition of her own and others' suffering. She apologizes to Ruth and Isabel for the unintended consequences of her actions or perhaps for the predicament she finds herself in, which indirectly affects them. It's implied that she feels remorse for the trouble caused and expresses this through an apology, even if she believes that her actions were necessary.
In various contexts, characters apologize to show their sincerity, admit their misunderstandings or wrongdoings, and to seek forgiveness. Such apologies convey the complexities of human relationships and emotions, reflecting the challenges individuals face when their actions, regardless of good intentions, cause hurt to others.