If I do shoulders on their own separate day should I do both GS and PUB shoulders? I know this is one of my weaker areas and need to improve them. Thanks.
Do you mean a separate should work PLUS GS shoulders and PUB shoulders on two other days?
IMO, that risks overtraining the shoulders (don't forget, they are also worked when you work chest and back, and plan your weekly workouts accordingly).
The shoulder joint is the most unstable in the body, and prone to injury. Overworking the area can lead to accute or chronic problems.
When a muscle group is in need of strengthening, it's important to give it enough time to recovery between workouts, so you can safely use your best weight for it. If you were to work shoulders, say, 4 days a week (which is possible if you do a separate day, then GS and PUB shoulders and then a back/chest workout), for most people that would not allow for enough recovery.
I personally find that when I'm doing a three-day split like GS, I get best results when spacing the two upper-body workouts as far apart as possible (especially since one works chest and the other back, both hitting shoulders). I put the lower-body workkout as the second workout of the week.
I will be doing the same with STS.
HTH!