How do I teach my rescue dog to do "her business" in a particular spot outside, and are some verbal commands better than others?
Teaching a dog to eliminate in a specific spot has little to do with placing a cue word ("hurry up") in front of the behavior. For two-three weeks make an effort to take her on leash to the area where you want her to go, when you are very sure she needs to go. Walk her back and forth, avoid verbal interaction and eye contact, which can be distracting.
If she doesn't "go" after five minutes of walking back and forth in an area of about 10-15 feet, take her indoors, sit down with her for 10-15 minutes and keep her by your side with no interaction. Head outside again. This usually takes no more than three trips outside. Give her plenty of praise when she does "her business!"