With a 5.5 hour schedule change, the customer would have the right to cancel for a full refund to the original payment method.

If I understand correctly, part of the problem is that he customer paid for four C+ seats and is being rebooked in regular coach for one segment. DL should do something (miles or vouchers) to apologize for this. Getting a refund won't work (breaking the fare) if they want to retain C+ on the other segment. OTOH, in the worst case, there are some seats in the very back of coach held for gate assignment for families wanting to sit together, although these seats could be in high demand on the Alaska flights this summer.

This is another case where it can be helpful to research available options on DL and then call and ask. Would connecting through ATL give better schedules and better aircraft? IIRC someone else mentioned an ANC-DTW flight this summer, so that could be an option too.

If the kids aren't too tired, five and a half hours at MSP is more than enough time to take the light rail downtown (Mill City museum is an easy walk) or to the MOA (indoor amusement park and aquarium in addition to shopping and restaurants). The Northwest History Centre (small airline museum) is even closer (it's about a block from the American Boulevard light rail station in the MOA direction from the airport), but I don't know what it's post-pandemic opening hours are. IIRC light rail tickets are valid for two hours, so you could just hop off there to quickly check it out.