J.B.
Your son smearing boogers on his face won't give him pink eye. It sounds like Dad hasn't properly disinfected something your son always comes into contact with at his house -like a pillow, stuffed animal, etc. He needs to thoroughly wash and sanitize EVERYTHING your son touches, sleeps on, wallows around on, etc. Of course he could have originally picked it up at daycare or gotten it more than once there. You should make sure they're properly sanitizing everything as well.
It is possible he's allergic to something on the pig farm or that he's touching something with fecal matter on it or something of that nature out on the farm and getting it in his eye -therefore setting up infection. Talk to him about watching the boy carefully. Also make sure that you have cleaned and disinfected all bedding, pillows, furniture, stuffed animals, etc. at your house.