For the best chance of getting sharp shots with a MOVING subject, typically you should use continuous AF (AI Servo on Canon), coupled with continuous shooting mode (to capture multiple shots so you can choose the best one later). Up to you if you want to use single focus point or auto focus point - they both will work if there is nothing between you and the subject to worry about. However, for portraits, it's more accepted to use a single focus point ... placed over the eye nearest the camera.
For a STILL subject, "One Shot" focus mode should work fine (not AI Servo). And it's your choice if you also want to use continuous shooting to get multiple shots.
In either case, the depth of field will be extremely narrow at 1.8 aperture, and it's very easy to get misfocus if you move the camera off plane even slightly. For such a narrow depth of field, you should continue using a single focus point (as you stated in your comments), and get the single focus point over the eye closest to the camera. Additional things that help with sharp focus is your camera holding technique, steady hand, steady base, smooth shutter press, etc.
I agree with Harry's comment that photo #2; however, does not suffer from a missed focus point. If you were using single focus point and missed focus - SOMETHING in the shot would be in focus - just not the thing you wanted. In photo #2, the entire picture is out of focus. Even with a narrow aperture of 1.8 and you missed her eyes for some reason ... her nose or face or hair, something would be in focus. With the entire picture out of focus, something else must have happened to change the focus significantly. Maybe you have a lens that allows full-time manual focusing, and you bumped or turned the focus ring significantly before taking the 2d picture.
In direct response to your listed alternatives, you should be well able to get sharp pictures, with great bokeh at wide apertures. Portrait photogs make their living with this type of setup. The wide aperture will also give you a relatively faster shutter speed, depending on your lighting situation. So, I don't think #1 or #2 are the best options. #3 is where you should focus (oops, no pun intended). Use Aperture priority (up the ISO as needed if you don't like the shutter speed the camera provides) and improve your technique with focusing and camera holding.