we split pickups and dropoffs between us parents but FWIW I don't find dropoffs ot be "specila time" at all. honestly, they're rushed and unsentimental. However, pickups often include nice conversation and summaries of the day, as well at the chance to fit in errands or eating as part of that trip, so my vote is to be there for pickup time.
there are preschools for 2 year olds. The preschool all my kids attended goes from 2-6 and the schedules are 9-1 9-3 or 8-5:30 so there are absolutely families sending their 2s to half day preschool, at least in my town. (FWIW the ages my own kids started pre-k at 4, 3, and 2y9m. but 2y0m is the minimum)
Berkeley mom of 3 and President of Tender Cargo Baby Gear
and The Nurture Center Store and Resource Center 3399 Mt Diablo Bl Lafayette CA 888-998-BABY