I have two young kids, both neurotypical, and I've made several longish trips with them, when my DH couldn't take time off work, etc. As long as you plan well, and prepare as much as possible, why shouldn't you? I don't get it when ppl act like you can't take care of yourself and your kids alone.

Single moms do it every flippin' day. You know yourself and your kids, you know what you can and can't handle, and if you're used to taking care of your kids on a daily basis, I don't see why you can't do this. When I was sixteen, I drove from Tuscaloosa AL to Killeen TX with my 2 yr old nephew, by myself, to meet his mom (my sister). About a 14 hr drive, IIRC.
Depends on you...are you comfortable with driving long distances by yourself? Do you freak out if you miss your turn/exit? Are you good with maps and directions? Are your kids OK in the car for long periods? As I said, you can answer those questions best.
The train option sounds good, but if that's not an option, I'd say prepare prepare prepare, and if you think you and your kids can handle it, go for it.