definitely train legs at the gym.
so you've got 3 consective days at the gym, make the most of it!
maybe,
friday
squats
bench press
+additional exercises for triceps/chest (anything you want really)
sat
rest = EAT and sleep.
that's all you have to do on saturday.
sunday
deadlifts
press
+anything you feel like for biceps/back
you say you can do shoulders and legs at home, i assume you have some weights at home?
don't neglect legs man, go sprinting on alternate days. hill sprints, weighted sprints. up to you. also smash the bodyweight exercises if you've got no equipment. im thinking chinups, pullups, dips, pushups etc. perhaps invest in a kettlebell for quick workouts at home?
personally, i think having well-developed shoulders is pretty cool. so i try to press as often as i can.
it's really up to you what you feel like doing, what i've written above is just what i'd tell my friend to do if he was in that situation. just do something consistently, eat well, sleep right. don't let the 'only 3 consecutive days of working out' be an excuse. once you see the results and feel motivated, maybe you could change your lifestyle around so you can go the the gym Mon/Wed/Fri or something similar.
good luck man, just start lifting today!