Question for you: how do you intend to get to Las Vegas, Nevada? The Southwest Chief doesn’t go there. In fact, none of Amtrak’s trains go there and haven’t since the 1990s. If you see Las Vegas, it’s Las Vegas, New Mexico which is several hundred miles east of Las Vegas, Nevada.
If you know that, and still want to get to Las Vegas via rental car at Needles, CA or Kingman, AZ (or you actually want Las Vegas NM):
When my family took the Southwest Chief to see my sister in we actually flew MSP-Kansas City then took the train KCY - Lamy NM. Didn’t want to backtrack to Chicago. I’d suggest the same, or a bus. If you do transfer in Chicago, you will have to stay overnight in Chicago. The outbound Chief leaves an hour before the inbound Empire Builder arrives, and Amtrak will not hold a train that long for you. Even if it were the other way, I wouldn’t recommend a same-day transfer.