Because you also have the normal washer drain on the line, you should be able to tee (don’t use the straight cornered tee, use the curved corner tee) into it for the floor drain. It would mean pulling up the floor linoleum or tile.. alternately going up through the garage ceiling and cutting into drywall from underneath and using a ceramic hole bit for the floor. I would put a pan and drain into that because you can’t guarantee the slope of the floor. The floor will also not have any ‘borders’ to contain the spill and direct it to the drain. The normal drain should already have a vent associated with it. The other question would be where the trap is located.
