You now going to have to remove all that caulking, scrape off all that old cracked paint with a trianguler scraper.
Push on the skirt and see if it moves when pushed toward the wall. If it does any new caulking will just crack. your going to have to find where the wall studs are and add some nails or better yet some screws with counter sink heads so the holes can be pluged with wood plugs.
I would use Alex 230 caulking, Long lasting and is paintable.
Then prim and paint the area.