Depends, sometimes one or the other, sometimes both. The hospital I thought about using wouldn't agree (because of the type of scar I had) but the doc I saw was supportive but it was out of her hands due to staffing and blood banking issues.
The OB that I had a successful VBAC told me at my 6 week follow up post partum that I just need to hope for all girls with small heads in the future...so I switched!!! I found it very discouraging to hear from MY doctor any doubt just 6 weeks after I pushed a baby out! So, I have switched to an OB that when I told him I had a successful VBAC, he told me "you go mama" and when I told him about feeling the pressure of the clock (2 hour pushing limit that I had both times), he rolled his eyes and said, "some women just need more time and you're probably one of them, so now you know you probably just need more time. I'm okay with that, I just pushed with a woman last week for 4 hours!"
So, in my new doctor's eyes, having a VBAC already is a huge deal....my old OB, I feel like I almost could have had more restrictions than I had for the first one!
Statistically, a successful VBAC makes you a better bet for subsequent births. Your scar has been tested and your pelvis "proven" (especially important for women whose CS was for FTP/CPD: a VBAC shows that this really was a fluke).
There are OBs who won't do first time VBACs but will do repeats, too. (With hospitals it's usually all or nothing--from their POV it's all the same.)
Liklihood of UR drops to about 0.1% (versus 0.5%) after you've had a successful VBAC. Many doctors and MWs will attend secondary VBACs but not primary ones. Hospitals with VBAC bans don't make a distinction. Though they cannot legally force you to have a c-section (and you are protected by the EMTALA laws if you show up in labor) they can use scare tactics and provide a hostile invironment towards VBAC in general.
My OB was really encouraged after my VBAC 2 weeks ago...she made a point to mention to me after the delivery that if we decide to go for a third baby, she felt I could easily birth a 10lb baby vaginally. (DD#1 was almost 10lbs & a FTP c section-my OB & I always wondered if it was just a positional issue or her size that caused my issues 1st time around)
Unfortunately it can change at a moments notice with disregard to anyone's past VBAC history. Case in point: I have had 5 successful VBACs and yet was told by the Bozeman Deaconess Hospital in Bozeman Montana that I would NOT be allowed to VBAC there.
As my midwife put it when I asked her about it now that I'm pregnant with #3 (which will be my 2nd VBAC), "Once a VBAC, always a VBAC". If you are able to stick with the same provider who was there for your first VBAC, you shouldn't have an issue, right?
For me, I had to fight just as hard for my second VBAC as for my first. The arguments and rationale were different each time, but the issue was the same: who gets to decide what is best for me? the hospital where I had my first VBAC did not make any distinction at all. I was still very risky. And my VBAC doctor wasn't really supportive in the first place, so that didn't help.
The advantage for me was that my VBAC was so empowering, I worried less about the scare tactics and pressure from the staff. Hopefully, you can say the same!
I think that many anti VBAC doctors won't care whether you've had a vaginal birth or not, and some hospitals have an all out VBAC ban.
I do think, in general, it may be easier to find a doctor to support you in a second VBAC, but it definitely isn't a given.
My OB with my VBAC was not super supportive. She was the "whatever you want to do, but are you sure you don't want to schedule that c/s?" type. After I had DS2 though, in the delivery room she said "you should definitely do this again!" It was a very good VBAC