Those are nice photos. Photogenic kids, too. It looks like the top photo was taken at about 12:20 p.m. That’s a tall tree, it probably reaches the ceiling. I imagine it’s around four to six feet behind the ottoman the child is on. There could be a softbox at camera left, but it might be a picture window.
Use low ISO, 100 or 200 is probably enough. To get the bokeh effect you will want a fairly large aperture and long-ish focal length. Focus where you expect the child to be. Adjust shutter speed to get the tree the way you want it. Then introduce a strobe with softbox, to blow light across the scene, in front of the tree, keeping it off the tree. Move the strobe around and adjust power to get the desired effect. You may want to put a grid on the front of the softbox, or you may get away with aiming the softbox between camera and subject.
You are not relying on shutter speed to stop motion. You are relying on minimal ambient light and a very brief flash to stop motion.
Let us know how it works out.