Child booster seats are designed to be secured with a lap belt. If you use a shoulder harness, you have to use the metal adapter to keep the seat belt from trying to twist the safety seat into the middle of the vehicle.
When my kids were little, they were ALWAYS in their booster seat in the middle seat with just a lap belt. ( a trick to make sure they are good and tight, is to put your knee in the seat when cinching the lap belt so it is good and snug.)
As long as you have the lap belt snug and the seat isn't moving around, there is no safety issue with just using a lap belt. Just make sure you use the restraining harness in the booster seat for the kid!!
Your wife should have no issue as long as the seat is secure.