Back routines: The exercises you have are good. You may want to consider adding in some chin-ups with resistance bands for assistance because chin-ups freaking rock and as a woman it's a huge self esteem boost to know that you can do a real chin-up. Machines don't cut it as far as training the same motor patterns that allow you to do a chin-up. It was only after doing chin-ups with resistance bands that I was able to get a real chin-up for the first time. You basically take a band and wrap it around the bar and your knee. It gives you a little extra help. Have her keep doing sets and reps until she gets to about 4 x 12-15 with a band. At that point, give her a smaller band that doesn't help as much and build back up again.
As far as actual routine goes, in my experience, with myself and my clients, I have seen a lot more progress with full body routines. Most people, but people new to lifting especially, benefit greatly from the added frequency of hitting every body part each time you hit the gym. Think about it, if you only have 1 back day a week, you are not going to make as much progress as you would if you have 4-5 back days a week. And if you have a whole hour dedicated to only one body part, the quality of the first few sets will be good, but then will start to go down. You won't be able to use as much weight, you're tired, your form might get sloppy, etc. It's kind of like studying for a test. It's better to study for 30 minutes a day instead of cramming once a week and never looking at the material again until the next week.
In each workout, I like to have an upper body push, upper body pull, leg movement (sometimes 2 leg movements: a squat movement and a hip hinge), core movement, and maybe arms or calves if I have time. I'll super set upper body with lower body to give adequate rest between sets.
I've gotten ridiculously strong from this routine, my husband has gotten ridiculously strong from this routine and I have a client who is 54 who can do 3 chin-ups and sets of 10 chest to ground push-ups after 3 months of training from this routine.
For the chest, shoulders and triceps, I start my clients with the following dumbbell exercises:
DB Bench (all the way down to get as much stretch as possible) 4 sets of 8-15 reps: I start with a weight that is challenging, but can be completed with at least 4x8. The next time they do this exercise, I increase the reps to 4x9 and so on until they can get 4x15 and then I increase the weight by 5 lbs.
Single Arm standing DB Overhead Press: I love this exercise because it engages the obliques and also prevents people from leaning back and arching too much. It also requires less coordination than 2 arm presses. So that can be useful for someone just starting out.
DB Incline Press: Same thing here as the DB Bench.
Sometimes I will substitute push-ups for DB bench (which are both horizontal), but basically, I try to hit every pressing plane throughout the week.
I also try to have the pulling movement mirror what they did for pressing. So if they do DB bench (which is in the horizontal plane) I have them do DB Rows or some other row that is also in the horizontal plane. Or if they did overhead press, I might have them do chin-ups. You get the idea.
I hope this is useful. Let me know if you have any questions. Good luck! Congrats on getting your girlfriend lifting. I love seeing women get stronger and develop confidence from lifting.