Whatever you need from your purse while you are in the middle of driving can be either set aside ahead of time, or reached for by the child in the back seat. You can also put the child in the front seat in charge of the handbag, which takes away some of the allure of the front seat.
With a 14 year old who will want a learner's permit in a few years, you want to set a good example of NOT being distracted and reaching around for stuff while driving with one hand - believe me, that's the part they will see and they'll think nothing of taking one hand off the wheel because they think driving is so easy! They don't realize what's required to focus on the road ahead and the other drivers. I found that out when my son started driving and believe me, I wish I'd been much more clear about that when he was taking up my habits. The first time he skidded off the road, we learned the value of that! So this is actually a good time for you to be commenting on other drivers or road conditions: "Look at that guy who pulled out without stopping at the stop sign! Good thing I was paying attention!" or "I wish that guy behind me wasn't tailgating. It's so dangerous, and his headlights are blinding me. I'm pulling over to let him pass. I'd rather get there one car later and be safe." Those things make an impression on teens, even though you may not see it right now.
I put my purse in the back seat and put my phone and sunglasses in the cup holder or one of the other storage areas up front. I don't need toll money because I have an EZ Pass, but there's usually a little place for toll money in the console or another little compartment. I have a pen and notepad attached to the sun visor but even so I only use them when at a stop light or when pulled over. I can't think of anything else that's in my purse that I would need while driving.
You could also consider something a lot less expensive for everyday use, and save the expensive things for going out, but even so, it doesn't solve the problem of being distracted.