Ask your mother to do some research on physiological third stage and the speed that syntocinon works. If she does this she may find that she is willing to only give you the injection if you bleed and not because there is a small chance of bleeding. You may also want to look at the effectiveness of breastfeeding in stopping bleeding.
Funny you should mention that - it was actually something mum did say - that encouraging bubs to feed will actually encourage uterine contractions because of the oxytocin release so that can be used. I'll ask her about the speed of syntocinon because if it is fast acting, we can then play it by ear.