close to delivery!

So on my dads side C-sections run in the family because they don't dilate at all and my mom had trouble with dilating but did it naturally! I'm 38 weeks and I felt like it was more open down there but when the doctor checked it wasn't even open at all! The doctor said it was really soft but not open then she brought up what will happen if I have to get induced! anyone else have this problem and had to have a c-section?