I'm sorry that you're going through so much right now, and adding the driving issues to that - that's really scary. Yikes.
Do you ever talk to yourself/your parts? Awhile ago, I noticed that I was having a weird problem when driving - I would get very, well, unskilled. Like, it took a lot of effort and concentration to keep the car going straight and to stay in my own lane, which is obviously not normal for me. When I thought about it, I realized that it felt very much like when I was a teenager, first learning to drive, when you still have to pay attention to *everything* because it's all new.
When I feel like that, I actually go through an internal dialog with myself. First, I ask my brain to please make sure that the "most adult part of myself" is in control and driving. Then, I very purposefully remember the last time I had a car accident, and what a pain it was. It was incredibly stressful... my car was in the shop for nearly a month, I was stressed about getting my car back, I had to go to the chiropractor a couple times to get my neck straightened out, and dealing with the insurance always sends my stress levels through the roof. The accident wasn't my fault - but the amount of stress was *enormous*, and something that I'd prefer to NOT repeat. I think through that, remind my brain of that, and point out that by having the most adult part drive, we can reduce the risk of having to go through anything like that again.
If you feel resistance from smaller parts, you can add some reassurance of something fun you might do when you get home safely, if that works for you.
I don't know if it will work for you, but it's helped me - it's subtle, not a big dramatic change, but over the course of a couple minutes, I get to feeling more "normal".
The other thing that struck me... most of the time, from what I've heard, when we dissociate, our brain is acting to protect us. Someone, a long time ago, posted about asking their therapist if they were worried when she left sessions dissociated, and the T was't, because they felt like their brain would work to keep them safe when driving.
But, it sounds like that's not happening for you. You mentioned being severely depressed...
Like I said, I'm sorry if that adds to your stress/worries, it's not my intention. But please, please if you can - talk to the T that you're still seeing, and see if you can talk through this (if you think it might be an issue). And, if you think it's a particular part and you can talk to that part about why this isn't a good idea, that might help too.
*hugs* I hope things get better for you soon. I know it sounds like a cliche, but please do what you can for self-care - be patient and nice to yourself

and if there's anything you can think of that sounds relaxing and nice, please indulge a little

Hang in there...