There are a couple of answers that could be correct here, depending largely on where your family lives.
First of all, if the family lived in town, it would be very likely that the church would have been close enough for them to walk. Towns were not very big back in those days and so it would have not been worth it to go to church using some sort of transportation.
If the family lived out in the country, it would likely have traveled to church in either a wagon or a carriage. A wagon would have been for a less wealthy family, or maybe for one that didn't want to show off. It would have been an open vehicle with no roof or other protection from the elements. A carriage would have provided more protection, but would have been more expensive.