Help needed Copper to plastic
I am rebuilding the second floor bathroom in our 1967 2 storey house. The question I have is regarding the drain on the bathtub. I have a new tub that came with a 2" plug/fitting. The drain/trap in the picture is 1.5" copper. The drain line runs between the joists (2x8) for about 5 feet the down the wall to basement where it joins with the main stack. The other pipe is from the sink in the en-suite bathroom which shares a wall with this bathroom. This drain joins with wye adapter 2 feet further down the line. All plumbing in this house is copper.
Most of this is pretty accessible as I am in the middle of replacing floors on the second level and gutting the basement.
Am looking for some advice on connecting this drain. Also, the current drain doesn't line up with new tub exactly, is off by 1.5", so it will need to be moved.