Well, I likely would have given birth in the car if I hadn't been using every ounce of my will not to. I'll let you know some of what came up for us and you can think about what might be problematic for you (or not)....As I said, it wasn't my intention to birth in the car, rather I had planned a MW-assisted waterbirth in an alternative birthing center that was housed within a hospital about 35-40 min from our home. My labor was short and went from very mild "could this actually be labor?" cramps to loss of mucous plug/transition very suddenly.
We got into the car mere moments after it became quite clear that yes this WAS really labor, and in a big way. Unfortunately this was just about 6 am in the suburbs of Chicago and our hospital was just outside the city so we were in rush hour traffic most of the way and it took us about an hour to get to the hospital. This was very stressful both for myself and for my husband, which is really not a safe way to be operating a vehicle. We couldn't really work together or support one another because he was trying to get to the hospital safely (and quickly), and I was trying to assess the baby's progress and plan how I was going to deliver it by myself should I need to. I was doing periodic internal checks (I could feel the head) but it would maybe have been helpful if I (or someone) could have seen what was going on too.
I also had horrible back labor and I remember desperately wanting someone to massage/apply counter pressure to my lower back, but DH couldn't since he was driving. It was so awful to be in pain and not be able to move freely into positions that felt better (walk, stand, squat, all 4s, sit on birth ball, whatever) or have somebody to help me in whatever way I needed.
Lastly, I DO NOT have a bleeding disorder (I've been tested multiple times) however I hemorrhaged at the birth right after DD was delivered (and again 2 days later). I had 6 units of blood transfused over a period of 2 days and my level still dropped to a 4. Now, I can't say if I hadn't received interventions immediately that I would have died (maybe if I'd received medical attention an hour later the end result would have been the same, maybe it would not have. Don't know), but it's a distinct possibility. I will say that had I started to hemorrhage and it had been up to DH to notice this, respond, and get me the attention that I needed while also managing our newborn, the experience would have traumatized him to a point where I don't think he'd ever be willing to have children again. As it stood, our experience was traumatic enough that he still gets triggered driving down the stretch of road toward the hospital, talking/thinking about the birth, etc.
FWIW, I DID get to the hospital and was fully effaced, dilated to 10, and at +1 station. We begged the MW to try to fill the tub and DD was born into the water moments later (before the hemorrhage drama began). All in all, we had no reason to believe that my birth would have any complications but it did and I am very glad that we had medical professionals and necessary equipment available to respond to my needs so that I could get to enjoy being mama to my girl (and now girls).
With your known medical history, I'd be dubious about trying to birth outside of an "intervention-ready" environment. I don't discount your fear of hospitals-the extended time that we spent in the hospital after DD's birth was rather awful to be honest, but I think that for me at least, the key was having a family member/support person with me (and DD because she roomed in 24/7) at all times so that they could respond to our needs and advocate on our behalf as needed.
I wish you lots of luck!