> to the point where I am not super comfortable driving with them. Running stop signs and red lights is a frequent occurrence
You're almost certainly right about that. Accidents in general [1] and car accidents in particular [2] are more common for people with ADHD.
The part you're missing is that the stimulant medication _improves_ the situation.
Quoting from the results of the second study referenced above:
> Compared with individuals without ADHD, male ADHD patients [...] had increased risk of serious transport accidents. In male ADHD patients, ADHD medication was associated with a 58% risk reduction [....] Estimates of the population attributable fractions suggested that 41% – 49% of the accidents in male patients with ADHD could have been avoided if they had been on treatment the entire follow-up.