Grab a Mears Taxi van from your resort. If there are no vans on the stand, the doorman will call one for you. If you need babyseats tell the doorman and he will make sure the van comes with the seats. Don't take a flatrate, have the driver run the meter.
When you leave universal just back to where you were dropped off and there will be taxis on the stand just as you come down the escalator from the walkway. Usually they are Mears. You can request a Mears taxi with babyseats if you need them and you will be back on your way to the resort.