LOL!! This suddenly gave me an "Ah Hah!" moment. Of COURSE there`s a business idea to shuttle a dog around, back and forth, with visitation rights! Today`s couples routinely get divorced, then re-married, and have kids going all over the world back and forth.
If you have time-share kids, why not time-share dogs? Then you can live in your time-share condo, take a time-share vacation, go back to your job-share job, and get involved with the spouse-share (discreet) club down the road.