You unlock Mom's Contact by picking up Moms Eye and another Mom item in the same run. Items that count towards this are
Mom's Heels
Mom's Lipstick
Mom's Bottle of Pills
Mom's Pad
Mom's Bra
If you picked up an activated item (space bar item) before Mom's Eye you don't need to hold onto it so long as you pick it up it will count towards it. As soon as you pick up the second item it will unlock.