I would like to add a utility sink in my garage, opposite the wall of my laundry room in a one story, concrete slab house. Can I tie into the existing washing machine drain/vent and water supply? Also, the water supply lines are plastic--what is the best way to connect to them, and can I connect to them below the valves with a tee? I understand that adding a tee to an existing drain must be a smaller size, but will I have trouble with bubbling, noise, or proper operation of the washer drain?

Do you plan to cut your tee into the washer vent and let the washer be wet vented?
I can see no drainage problems with that. As for the supplies why not swap the angle stops for double outlet angle stops,(see image) Good luck, Tom