Just like paint doesn’t stick well to really smooth plastic, you need to give a surface a little “tooth” to a smoothly painted surface for more paint to stick. And there is another issue that also has to be considered which is airborn oils and dirt. Things like cooking generate these and the oil/grease lands on your surfaces and also doesn’t let new paint stick. The first thing to do is to wash the surface to be painted with a grease cutting cleaner like Dirtex or TSP, following label directions. Then, you can “scuff sand” to roughen the surface. This sanding does not mean removing all the old paint, just slightly roughening the surface of the old paint.
A good way to do this for “curvy” surfaces is to take a quarter of a standard 9″ x 11″ sheet of 220 grit sandpaper and fold that into thirds. The tripled thickness makes holding it easy and you just refold to get to a fresh sandpaper surface. For wider flat expanses, use a sanding block. Remember that you do not want to remove paint, just roughen the surface that is there. The sanding of a full lenght stairway going one floor should not take much more than an hour. Then, vacuum up any dust that you have generated and you are ready to prime. Follow the primer with a coat or two of paint.
I’m not sure what you mean by “satinwood” paint. I assume that you mean a satin finish paint–between a glossy surface and a really flat surface like a blackboard has. If this is not correct, let us know.
Henry in MI