If all parties have express, they go through the express line together. Near where the ride loads, there is a baby swap area. One adult goes to babyswap with the baby, while the other adult rides with the other children. Then when the riders get off the ride, the adult goes to babyswap room and stays with the baby while everyone else goes almost straight onto the ride. Technically they get in the express lane but at a point that is very near the load area so they don't go to the end of the express line or anything.
If no one has express, they wait in the standby line and once they reach the load area the adult goes to baby swap with the baby. Once the party rides, the adult who was in the babyswap room (plus the other riders) go into the express line near the ride area while the other adult stays with the baby. This keeps them from waiting in line twice for the same ride.
Unlike Disney, the babyswap area is very close to the ride load area. It is usually an airconditioned room with chairs. It usually has a glass so you can watch your family load on the ride.