She was holding back her tears, swallowing her pride just for the benefit of her daughters.

swallowing 是动词 swallow 的现在分词形式，原意是"吞咽"，这里用作比喻义表示"忍受、咽下"。 her 是代词 she 的所有格形式，表示"她的"。 pride 是名词，意思是"自尊、骄傲"。 swallow one's pride 是固定短语，字面意思是"咽下自尊"，比喻"放下身段、忍辱负重"。