Line 2 will never run in CP corridor and it is a dead thing period.I'm talking about replacing the Milton Line with something fit for purpose: that is, regional rail connecting Mississauga and Milton to Toronto with fast, frequent service. HuLRT does not fulfill this mission. It is primarily for connecting people along the Hurontario corridor, and does not serve West Mississauga or Milton at all. I did not mention using Hurontario for the alignment. If anything it should be further west, and hit MCC on the Western end, which is where the current centre of gravity if for MCC and the part that is poorly served by HuLRT.
All that said, I refuse to believe it is 'impossible' to come to some arrangement with CP for the Milton Line corridor, and that Line 2 extension to Sq One would be a foolish use of resources given the alternatives, at least until the Dundas BRT reaches capacity in the distant future.
CP corridor can support both CP and GO with 4-5 tracks easy. The main issue is the cost to do it as it will be on ML dime with CP charging an arm and leg to do it. You had some 3rd track installed by 2007 and then went off the rail. A few bridges have been widen to support 4 tracks in place of 2 with Hurontario St still waiting for 2 bridges today.
There are a number of locations that will cost big bucks to grade separate the rail corridor starting with Mississauga Rd crossing since it is on a curve and will require a number of places to be torn down as well building new roads to replace the ones that have to be close..
At one point, there was an option of building an branch line to Orangeville and could happen down the road, but currently dead at this time.
You will not be around to see Line 2 going to Sq One and most likely your kids as well. Been 50 years since the Line 2 made it to Kipling.
You can build an branch line off the Milton Line to Sq One as a bypass costing big bucks since it will have to be tunnel 100% unless you do a Tram-Train using Hurontario LRT line.