I just did something quasi similar to this, but with two kids. What I did was booked my son and I on one PNR using ecredits and then put my wife and daughter together on another using miles. I called DL to connect them - and they say they did - but I still do not see their names when I look at my reservation. Either way, that's not important. The important thing is that if the poop should hit the fan and we get split up; both kids will be with a parent.

So in your circumstance, I'd use the ecredits for you and the child and then use your miles for your wife. I recall getting a warning about an unaccompanied minor once when I tried to use points for one of my kids on a separate reservation. I immediately said to myself "I'm not dealing with this", backed out and booked it as I just mentioned. Maybe it's a cinch to bypass that, I don't know... Did you try calling in?

Lastly; with points never expiring, go ahead and sign your kid(s) up for an account so they can start earning. As much as I'd love for both my kids to hit 1MM by the time they head to college, realistically they're going to be in the 600-700,000 lifetime mile range. Just be aware that ecredits will go to their account if you cancel non-refundable tickets, so you'll need to remember to go to each child's profile and apply them when making future bookings.