Not really, dependent on the sisters own caring commitments. Which means she would potentially have to leave her own family which may not have been possible, or take them with her, putting even more people at certain risk. DC moving his own family and isolating with outside support is safer then her coming to him and making the risk of her getting covid pretty much a certainty, rather than a possibility.
Healthy people travelling door-to-door with toilet stops to care for a child would not put more people at risk than unwell people travelling door-to-door with toilet stops. If he needed childcare then law allowed for someone to come and give that care, or could have taken the child to them.
It's utter nonsense of him to suggest that he needed outside support like the shopping his sister brought. Not only is he wealthy, but he's part of the government. There's no way he needed someone in Durham to go to the supermarket for him because he couldn't get a delivery slot.