I'm thinking of adding some extra arm exercises at night (nothing too crazy, just some more pec/triceps to help my arms) as well as my normal routine in the mornings which I have a protein shake with water after- my question is would having a second shake after the evening workout aid my recovery time or would it just hurt my weight loss? I wouldn't want to overwork the same muscle groups twice a day but if I used other muscles in the morning workout that would be ok right?
so long as your giving each muscle group enough recovery time before working them again it should be ok. having the extra protein shake would depend on how much total protein you are getting throughout the day and how the calories fit into your normal diet.
for a strength training athlete you need 1.2 - 1.6 grams of protein per kg of bodyweight per day
more importantly you should be having some carbs within 20 minute of your workout to aid recovery and protein within 2 hours.