I haven't worked with split designs. Usually designs were split due to stitch counts and hoop sizes.
Do you need to bring the individual part into the machine? You would delete part ONE since that is already stitched.
Tell the machine you want to stitch part TWO and set it to stitch out.
Then delete part TWO and bring in part THREE to stitch.
It looks like there are reference cross hairs on the designs. Did the cross hairs stitch out on design part ONE? They are used to match up design placements from multiple designs.