My wife has a SkySaver ticket which involves flying Alitalia metal from ORD to VCE by way of MXP. Her return flight is on Delta metal from BCN to ORD by way of ATL. The Alitalia flight on the SkySaver award is shown as an Alitalia flight and not a Delta code share.

We are thinking about having our daughter fly with her on a purchased ticket. I noticed that we can buy the exact same itinerary thru Delta but the Alitalia flight is shown as a Delta code share.

Is there any drawback to having the two tickets setup like this? Specifically, if there is some kind of problem that my wife and daughter encounter on the Alitalia flight (missed flight, late flight, cancelled flight, lost bags, etc), will my wife have to deal with Alitalia while my daughter would have to work with Delta? My main concern is making sure that the two of them are able to travel together should a problem arise.