I transferred an NCL. For NCL you have to email them the transfer request form with your Chase TA info, then NCL will change the booking. Mine was crazy quick, completed within a couple hours, but I think most are within a few days and I think the page said may take up to a week for that department to process it.
Depending on the ship, NCL is good with kids too. I've seen some reports where the kids loved it including the kids clubs and others where the "club" was just an open room they may have some activities in. So I'd do research for reviews of the particular ship you're looking at. I know for Bermuda that had an older ship and a newer ship going depending on the port you left (Boston or NYC). That said, we cruise
DCL without kids. There's enough stuff to do for adults, including adults only venues, so the parents can get some quiet time in too. The one complaint for DCL is usually the pools, they can be small compared to all the kids that want in. They have an adults only pool though, if sitting on the deck is important. We've done both equally and pick one or the other depending on why we want to cruise that time. We've done both cruises you're looking at, actually. Tough choices