I do the EZE-AEP transfer and head on to SLA a couple of times a year. No idea if LAN offers transfer service for biz class, but in my experience the standard warning from the airline is that "you're on your own" as far as getting to AEP.

With a family of four, the easiest way would be to head straight to the Manuel Tienda Leon kiosk right outside of the customs area (once you pass through the frosted glass doors past the x-ray machines) and get a private car to take you directly. Last time I used the private car it was 180 pesos direct to AEP, but with prices going up everywhere I'd imagine it's more now.

I'd agree to allot 90 minutes for the trip + traffic, although really I don't think it's ever taken me that long. It's basically a fixed-rate taxi and will take you right there. The bus is a cheaper option but is slower as it goes through the middle of Bs.As. to make a stop at Retiro bus station...not a good option if you're on a tight schedule. There are random taxis outside of the terminal but it's an iffy option.

Checking baggage at AEP on LAN is always a nightmare...the lines are a mess, there is no organization, etc. The only time I've ever cut it close making my AEP-SLA flight was having to fight through the clueless crowds and lines in front of the counters at AEP to get my baggage checked.

If you have pre-printed boarding passes and only carry-on luggage, once you get to AEP it's a breeze to get through security and to your gate.