My children's father has a suspended license and no vehicle. He filed a petetion for timesharing. Who's responsibility is it to transport the children

 Certainly you do not want a person with a suspended license driving your children, nor does the court.  However, lack of a license does not mean he gets no timesharing. Typically, the transportation responsibilities are  shared by both parents.   What typically works nicely is that the parent beginning his/her timehsaring picks up the children.  So when the father would begin his timesharing, under this arrangement, he'd pick up.  Absent a license he could ask a friend or relative to drive (who has a license) or he should get an Uber account.  Then, when the father's timesharing ends, you would pick up, becausd you'd begin your timnesharing.  YOu might want to suggest this arramgement, and make sure to include he cannot dirove with a suspended license (he might at some point have it reinstated) and that the transportation is shared- as I suggested above, if you think that will work for you.   Best of luck, Cindy S. Vova Law Offices of Cindy S. Vova, P.A. Broward: 954-316-3496 Boca Raton: 561-962-2785