many people on here will talk to you about the dangers of induction and are anti-medical intervention unless absolutely necessary, and it is worth listening to their views.
HOWEVER, the psychological impact of going to 42 weeks when you really dont have much support for very long should also not be discounted...
so in the end, it should be your decision.
one option to get the drs to take you seriously is to see a psychologist/social worker/counsellor, and explain your situation and see whether they will support you by writing a letter saying that there are valid reasons to request an induction.
good luck