Where is Mattie Cook sent to?

The answer to your question can be found in chapter 10. With the fever spreading like wildfire through Philadelphia, it is decided that Mattie will be much safer if she goes out to the countryside. After consulting with Dr. Kerr, Grandfather agrees to take Mattie to the Ludingtons' farm, which lies some distance from the city. They leave in an old coach-wagon, accompanied by a farmer and his wife and infant child.
However, in the following chapter, when the wagon reaches the town of Pembroke, they are stopped by armed guards and a doctor, who are intent on preventing anyone with the fever from entering the town. Unfortunately, this is when Grandfather has a very ill-timed coughing fit, and the doctor, concerned that they are carrying the disease, orders them to turn around and return to Philadelphia. Mattie and Grandfather are expelled from the wagon and left by themselves on the country road.