GO has moved stations before.
Unionville Station used to be in the historic village. It was moved because GO (and many of its customers) wanted a giant parking lot (in the long run, it makes a lot of sense; Highway 407 buses can serve the new Unionville Station easily; Markham is urbanizing the area, including a new university campus). Trains that stopped at Lorne Park were moved to Clarkson soon after GO's launch in 1967. Weston and Miliken Stations were moved across the street (Lawrence and Steeles Avenues, respectively). And of course, GO moved its Downtown Hamilton station in 1996.
But there's room for both Mimico and Park Lawn, even with GO's current model of 10 and 12-car diesel trains. Other stations in close proximity include Centennial-Markham-Mount Joy, and Maple and Rutherford.