My laundry sink and washer are connected to the same water line by a y-connection and I want to be able to turn off the washer water to increase the pressure of the laundry sink water. Or should I shorten the water lines to the laundry sink to increase the pressure.

None of those are going to increase pressure. THe washer isn't affecting pressure when its not intaking water (filling itself up)... and you don't want to be turning off water to it when it is.

DO you have pressure issues at any other points in the house? If the answer is no... start looking for valves that aren't all the way open.

If filling the washer cuts down on filling the this is not a pressure issue but a volume problem. This is a common complaint with older houses with galvanized piping. Over the years rust builds up in the pipe walls,(see image) cutting off the volume of water. You will have pressure until you start to run out of volume.
There is no easy fix to this. I had the same issue in my 60 year home.
There's only one solution and that is to have your house repiped in plastic.
Sorry I couldn't give you better news but all of us with older homes are faced with this problem somewhere down the line. Good luck, Tom