According to signalled paper, you may be able recrystallize L-alanine isopropyl ester hydrochloride from cold anhydrous dichloromethane (0 ºC), possibly evaporated under reduced pressure and in the absence of water vapour: http://pubs.acs.org/doi/abs/10.1021/jo201492m
I believe you should be ablet dissolve in minimum amount of DCM and crash it with hexanes and was it with several times with hexanes you should be able purify the solid. I ourified and crashed several amino ester salts with that way alanine should also work fine.
To purify your product dissolve your product in water then neutralize it by adding dilute solution of NaOH, filter . Then acidify the pure filtrate with HCl, your l-alanine isopropyl ester HCl will form again Good Luck