Wow, I would seriously report your first doctor. Induction places the baby under increased stress, and also puts the mother at higher risks of complications. Sometimes it is medically necessary, and most doctors prefer to do it if a baby is particularly late to avoid the complications that can come from an overly-large baby, but a doctor inducing you one day after your due date, unless there is a medical reason, is a doctor who had plans later that week and didn't want you to interfere. It wasn't in the best interest of you or your child.
As a disclosure, I have been induced with both of my children. My son was induced after 10 hours of natural labor because the labor was not progressing. My daughter was induced 9 days after her due date because her stress readings were starting to concern my doctor. I am not against induction and I'm not a "natural childbirth" kind of mom. But I also am truly disturbed that your first doctor induced you a day after your due date, as though your due date was some sort of expiration date instead of an estimated date AROUND WHICH the baby should be ready. Believe me, you'll survive another couple of weeks of pregnancy if the baby doesn't come earlier, even if it's not terribly comfortable. Your body and your baby usually know when it's time, and statistically, most babies need slightly longer than the 38 weeks (excluding the first two weeks of your cycle).
Good luck.