Yeah, don't do any mileage transfers. Just call in when you are ready to book and ensure enough miles are in each account. It would help if you could do it as a three way call with your wife also on the phone. This is the ideal way to do it. Just tell the agent the situation. They will know the mechanism of how to ticket it and link the reservations.

If they tell you that you must pay to transfer miles (which I don't think they will) Then tell them that you can book all 4 of you together using a combination of accounts and then your wife can cancel her ticket in the free 24-hour window and her miles/cash would get redeposited/refunded at no charge, leaving the 3 of you ticketed with no transfer fees. The agents know you can do this option, so they will make it easier up front.

I second the recommendation NOT to use Basic Economy fares/awards.