I think you should try to get a second opinion. Get as much information about the situation as you can and then make a decision.
There will be issues with the previous c sections as there will be the concern that the scar could rupture during labour. You will probably be quite stretched with a twin pregnancy too.
I had an emergency c section after being induced at 40 wks when I had my twins. I wanted to have a natural birth with my 3rd child but didn't go into labour so had to have another c section as they wouldn't induce as they were worried about the c section scar.
You need to make your own decision but in your shoes I think I would err on the side of caution. Who knows you could go into labour before 38 weeks and this will all be academic.