You won't have that problem incorporating Push pull Training,
See! doing Bench press works the tris,over head press works the tris, then incorporate a tri isolation workout at the end.
Next day You'll be doing pulls Lat pull downs and Working the Bis
The Tris are isolated so no stress is put on them.
Rows Works the Bi's, then incorporating an isolation bicep Workout to failure 6-7 sets.
I'm suprised your trainer aren't aware of this, goes to show Trainers are some times garbage!