I really feel for you, I can relate a lot to how you are feeling. I'm so sorry to hear you lost your sweet DD.
My DD1 (3rd DC) was stillborn at full-term, no reason found. It was the shock of my life, she would be 3 tomorrow :(
I have gone on to have two more babies, the youngest currently in my arms is just 9 weeks old :)
They were both induced at 37 weeks, mainly for my peace of mind. I completely freaked out at the thought of being induced and terrified myself reading stuff on the web.
Both times were very different but both completely fine. The first I had a pessary, 6 hours later after mild pains they broke my waters and he shot out in under 15 minutes! Because that was a little fast and furious for me I declined the pessary next time and had ARM and then the dreaded drip I had read so many horror stories about. It was fine, took a little longer but was more gentle. I managed with just gas and air, no problem.
Rallytog is right, the CFM is very reassuring, and I found all the staff hugely sympathetic to my worries because of my history.
I think the fact that you have laboured and birthed before will help, your body knows what to do so induction is likely to work better, and faster.
Good luck for next week. And please post back and let us know how it goes. I found that holding my baby after losing a baby was the most amazing thing, the relief that all was ok. I miss my DD and she will always be a part of our family, but a new baby helped to soften the rawness of the loss.
Will be thinking of you next week x