You should lightly sand the walls to dull the sheen of the satin paint which will help in coverage and wipe the walls with a damp rag to remove the sanding dust. Then prime with Sherwin Williams Prep Rite 200 latex primer and finish with at least two coats of either Cashmere or Duration Home from Sherwin Williams.

Hope this helps out.

Yeah strip it all the way down that it's the only way you can get a go white coat on top of it

You do not have to remove the red paint to get a good coverage with white. I am not sure what this previous posting is think about.