Well, unless there is a valid reason for you to be induced, you can refuse the induction. Don't show up, call and say you feel sick, etc. Why would they want to force a tiny baby out? Maybe she's not done yet!
If you end up willing to go along with the induction, you should know some things first. What is your bishop's score? If it is not favorable for a successful induction - don't do it, your body just isn't ready yet.
Also, you may want to do things for the induction that can be stopped. If they try cervadil first to soften your cervix (don't do cytocec, it sounds much more harsh and some think it can lead to uterine rupture) and then pit to get ctx going and those things don't work, you can turn it off, go home, and try another day. If they break your water, you're on a clock and can't go back. And from everything I've heard, pit ctx can be a lot more intense, faster and longer and stronger. But plenty of women get through it without pain meds. You can insist that they start you on the lowest amount in the iv, and then try turning it off when labor seems to be establishing itself.
Please, I know it is so hard when your care providers all act like you *have* to go along with their recommendations and they will do things to scare you by telling you your baby or your birth is in danger if you *don't* do what they say. But they rarely outline the risks in detail of what could happen if you go with the induction. Yes, you are more likely to end up with a c-section. You are more likely to end up with interventions. There are ways to check on the baby to make sure she is okay without forcing her out. 42 weeks is the *beginning* of being "overdue". You're not overdue when you hit 40 weeks. You are in charge of your body and you don't have to go with the induction if you feel it isn't what you want or need. If your body is fine and the baby is fine and you feel content to wait, then just stay home. The hospital can't refuse you care if you show up at transition when you're 43 weeks.
Go here to learn about your bishop's score:
http://www.mother-care.ca/bishop.htm
Sorry I wrote so much. It's a subject that really makes me upset. I truly feel almost all babies will come when they're ready and by forcing a deadline on women it just hurts them, it hurts their bodies their emotions and their early moments with their babies. To have to choose between a care provider that you want to attend your birth or a drug-free birth isn't a fair choice at all. It's one of the reasons I did my own prenatal care and birthed my baby on my own. The stress your HCP's are putting you through shouldn't be allowed. Try to negotiate getting NST's to monitor the baby after you go past 42 weeks (if you even go that long) and keep the induction for IF the baby is showing signs of distress.
I'm sorry you are going through this.