Seems to me, according to map-quest, they'd both arrive in San Antonio within about 30 minutes of each other, weather permitting
(EDIT - Thank you danni for the actual mileage and time, i had exited Mapquest already and was trying to remember)
I think this whole thing was set up by the Smith's. I think they know who has the baby, and that it's a family member or friend in Nashville or near there. I think that EJ might not actually have any idea who has the baby, aside from the hand off to an unknown (to her) person. It makes perfect sense to set up someone from Nashville to meet someone from Tempe... in San Antonio.
I also agree with an above poster that EJ might very well be singing like crazy, and it would make perfect sense for LE to claim that she isn't saying anything.