Is it permissible for one person from a married and financially capable family to offer the sacrifice, while the rest donate the cost of their share of the sacrifice to the poor?

It is permissible to share in the Udhiyah (sacrifice) under well-known conditions. If each person is financially independent or lives in a separate dwelling, then one Udhiyah is not sufficient for them. It is a Sunnah (recommended practice) for a financially capable Muslim to offer a sacrifice on behalf of himself and to include his household, and this is the view of the majority of scholars. It is better for a Muslim to offer the sacrifice than to donate its price, because he can combine both by donating a part of the Udhiyah.