I have driven diapered many times, and I am always grateful to be able to do so. Here's what works for me.
First, choose a diaper that is really absorbent. That may mean cloth with plastic pants if, like me, you are a sudden and heavy wetter (or more). Bring a diaper-bag with a wet-sack if you need to change discreetly while stopped somewhere safe. Knowing your diaper will work is essential to being comfortable using it while driving. Driving requires total attention, all the time, so it can be dangerous worrying about leaks while negotiating the highways and byways and watching out for other drivers and pedestrians.
Second, use a disposable, waterproof puddle-pad. That way, you won't wet or soil your seat (or the surrounding areas, such as floor-mats) if you do go in your diapers and they happen to leak.
Third, be aware of where you pee in the diaper. Cloth disperses wetness very well, given time, but too much wetness in one spot all at once can cause leakage. ('Sposies too.) A diaper-doubler properly positioned can work wonders. If you can safely shift positions in your seat while driving and voiding, that can help too. But safety first! Better a wetting or soiling accident than an auto accident!
Fourth, make sure your diapers are snug but not too tight. It can be challenging using a diaper while buckled-in (use those lap and shoulder belts all the time!), so make sure your leg-cuffs and waistband (on your 'sposies or plastic pants) are providing proper coverage and security as well as comfort.
Finally, be aware that urine is often used in tanning to cure leather. If you have leather seats, and you experience a leaky diaper (just a wet one), don't worry. Just wipe up the pee with warm water and soap when you get home, and all should be fine. I've wet my leather seats many times by accident (leaky 'sposies -- not a fan), and they are none the worse for wear, even after all these years.
Hope that helps. Drive safely, and happy nappies!