Does he feel bad? like, I mean remorseful that his forgetfulness could have harmed his children?
You call them "your" children in your post. Are they not his as well? Shouldn't you refer to them as "our children?" As in, he drove "our children to daycare and then had a seizure 1.5 hours later?"
You're not his mother. This is not your battle. You can't control it.
Of course he swore it would never happen again. He probably meant it (although I don't know him). I don't think this is a "trust" issue at all (he didn't intentionally lie to you), as much as it is he needs to have ownership in what the consequences are if he fails to control something that is controllable.
I would say this warrants a conversation. Ask him what he wants. Ask him as a responsible father what he needs from you, as a responsible mother, to help support him in BEING a responsible father.
This is about more than just driving..... Are you going to never leave him alone with them again? What if he is sitting with one of them on the couch and has a seizure. What if he is cooking them dinner and has a seizure? You can't micromanage his every move out of fear that he won't take his pills.
You can't just say "you're not allowed to drive the kids anymore". That's not a realistic consequence. Even though I understand why you are scared and that your motivation is to protect your kids and keep them safe.
However, my bf is bad about remembering his allergy pills. So, every night we take them together. I'm not his mom and if I say "I'm getting my glass of water for my zyrtec... would you like one also?" and he DOESN'T take his pill.... I don't nag or remind him again. That's on him. yes, I know..... it's allergies and the consequence is a stuffy nose or a sinus infection..... not the same as a seizure. But still.......
Just my $0.02