。
Mom's been sick for the past couple of days.
Literal
Mother [subject-が] these 2 days sick [explanatory-なの].
The sentence-final なの is explanatory + soft/feminine — な (copula linker after noun/な-adjective) + の (explanatory nominalizer). It's the casual-feminine version of ~んです / ~のです, giving the sentence an intimate 'I'm telling you, the thing is...' flavor. この２日間 specifies the span of the ongoing illness.