Yes, you can thin paint with water, but this may affect coverage and alter the integrity of the paint film. You are better off using a paint conditioner like Floetrol or XIM. XIM is better, but Floetrol will work. I would recommend a 3/8" nap if you are painting with a washable paint.

Most quality latex paints are somewhat thick. Consider pouring the gallon of paint out of its original container into another. You will see a small amount of paint left in the bottom of the original container. Add a small amount of water to this, generally about 1 cup. Stir or return the paint lid and shake very well to mix the water and paint at the bottom of the container. Now add this back to the original paint you poured out previously and stir very well. This should allow the paint to be applied without the orange peel look. As mentioned a 3/8 to 1/2 inch roller cover and a good sanding of the old paint job should leave a pleasant look.

Ralph Lauren paint is designed to look like that, watering it down will ruin that effect. Just get normal paint and skip RL and you will be fine.