Appleton Junction was on the west side of Appleton, where the old Milwaukee, Lake Shore and Western crossed the C&NW. The station there was one of three that the C&NW had in Appleton, and was used until the start of Amtrak.
I believe the TMER&L terminated at Sheboygan. The C&NW ran up the lakeshore from Milwaukee, through Sheboygan and Manitowoc to Green Bay, but I don't know if it ever "connected" to the TMER&L . . . I doubt it.
As an aside, the C&NW had a second route to Green Bay, the one through Appleton. Both routes had passenger service until the start of Amtrak.