Yes, you could have trouble with a "couple of cases." Chilean law allows a maximum of 2,500 cubic centimeters of alcohol to be brought into the country tax-free (I presume that's per person). I've never made the land crossing, but by air ALL luggage, cargo, etc. will go through the big x-rays and they will definitely see that you've got a large quantity.
Link is in Spanish, sorry:
https://www.gochile.cl/guias/guia-ch...y-aduanas.html