under same booking code, your baggages would be at destination city which is lax. no need to checkin at tpe. 2.10 hrs is plenty of time transit at tpe from terminal 1 to 2 (US/Europe flights departure at t2). returned trip 50 mins transit is little bit tough when you transit from t2 to t1. but make sure you checkin at transit counter once you arrive tpe. ground crew would help you out. no worry!