Hi Jes - true shoulder dystocia is quite unusual, and is more common with bigger babies but this is not always the case, as it can depend a lot on yours and babys position at delivery. Lying on your back or even semi-recumbant (sitting up at 45 degrees) is most likely to cause this, so its important to keep upright if you can.
Im guessing that you did not have shoulder dystocia with the first 2? If its any consolation, for all the times I have seen the team standing outside the labour room door, ready to jump in and assist at the first sign of sticky shoulders, I have only once seen them have to do much, as being prepared will almost certainly mean that there will not be a problem. Sorry if this is a bit anecdotal though
If you were to be induced at 37 weeks, (and I think you have a good case for this), it does not mean that you are not in control, I have been the midwife in many beautiful labours where the woman has been induced, had an epidural and the synto drip, and within a few hours, she has had a great experience of a completely painfree labour. It might not be exactly what you expected but it can still be a fantastic experience, especially if you can have a mobile epidural with wireless monitoring, (which we can use) and can still walk around the unit, use the mats / ball / birth stool, or just squat or hands and knees to deliver. Just no pain
I know this will not stop you from worrying, because that is natural if you had a traumatic experience last time, but if you can stay positive, Im sure things will be better than you are expecting. Good luck.