You can be induced, but most doctors won't unless you are past your due date. btw - I had a doula for my first birth and she was very little help. I would never pay the money to have on there again - my husband offered much more support than she did and once there were medical interventions necessary she was totally out of the picture.
You really need to do some research on a VBAC. They should not induce as it increases the chance of rupture. You should talk to your mom about coming sooner and staying longer. VBAC is just like any other natural labor plus they tend to watch you more. Your mom could act as your labor support doula. Do you maybe have a sister who could come to watch the other two kids? You could also call around and find a doula in training. Plus, you might need to change doctors. If your current doctor is afraid of VBAC you are going to need someone else.