Car stalls while driving, then restarts after engine cools about 10-15 mins

They likely had a reason to want to replace the EGR valve and they can be expensive but the distributor pickup will solve the intermittent stalling. This was so common that a lot of people carried spares in their glove boxes. If you don't like paying for the mechanic's expertise and experience, and the ridiculously high cost to the shop to meet all the government regulations and taxes, replace the pickup yourself. All you'll need is a screwdriver. There is nothing to adjust when you're done.

EGR valves can be cleaned but they can fail in a number of ways. To cause stalling at idle is usually a result of the valve sticking open and letting exhaust gas back into the engine. You won't notice that at higher speeds when it is supposed to open. The problem is the mechanic can't be sure there isn't something wrong internally with the valve assembly that can't be seen. If he tries to save you money by just cleaning the valve, and you continue to have problems, he knows you're going to be angry. He also knows you may go to his competitor down the road next time who WILL change the valve and solve the problem. Who will you be angry with? The guy who tried to save you money but didn't fix it right the first time, or they guy who just replaced the valve and fixed it? You're going to angry with the first mechanic and you will assume he is incompetent. Strike one for the reputation of all mechanics. We used to run into this all the time when I worked for my uncommonly ethical cousin in his tv repair shop. So often when we tried to save people money by cutting corners we ran into problems resulting in a second trip to their house. It didn't take long to learn to turn a blind eye to peoples' financial situations and just fix the tv right the first time, regardless of cost. It wasn't our fault the tv broke, and there was no reason to MAKE it our fault to not fix it right the first time.

Mechanics have the same dilemma. There is no benefit to them to cost you more money. In fact, every time I was able to tell a customer what they needed was going to cost a whole lot less than they expected, I was the hero, and they automatically assumed I was honest. But when I recognized the need for more parts than was expected, I had to do it right and explain why the previous person didn't catch something or why replacing that part was required. Simply taking the time to show and explain, (and I never got paid for that time), showed customers I had their best interest at heart and earned me a great reputation among my customers and my employer. This happened all the time when I was a suspension and alignment specialist. Owners would come in expecting the one broken part to be replaced but I had to explain that all the other parts were just as old and about to fail, and I had to show them why those worn and sloppy parts would make it impossible to align their car and get good tire wear and handling.

Like most doctors, mechanics don't have good communication skills with the public, but they DO communicate well with other doctors and other mechanics. We overlook that with doctors and lawyers and accountants, but with mechanics it's different. Because of a few publicized bad examples we assume all mechanics are disreputable until we learn otherwise, so I suspect many of them live down to your expectations.

Getting back to EGR valves, there used to be a pretty high failure rate with the electronic portion of that assembly due to moisture getting into it, but the only way to get that part was to buy the complete valve assembly. An experienced mechanic will recognize if your valve is old and likely to fail soon if it hasn't already started to act up, and given your description of the problem he had better be suspecting the valve along with the distributor pickup. He knows it's unlikely two totally different parts failed at the same time, and he is aware you won't be happy with the repair bill, but he also knows you're going to really be angry if that EGR valve fails during your upcoming trip out of town.

Given your description of the engine having to cool down before it will restart, that is the classic way the distributor pickups on a lot of vehicles act when they fail. They become heat-sensitive and work again when they cool down. If you don't want to replace that yourself, any mechanic at any independent shop can do that for you. If I was your mechanic I would explain that you don't have to wait 10 - 15 minutes to restart the engine if the EGR valve is sticking. Those do not fail by becoming heat-sensitive. They just fail, period, but they can also be intermittent and work okay at times. The engine will still restart right away though.

A younger mechanic who never ran into the distributor pickup problem before would be correct in not wanting to replace it without observing the stalling for himself and diagnosing the cause. I call that "replacing random parts" which is the least effective and most expensive way to diagnose the cause of a problem. That's what a lot of do-it-yourselfers do but we wouldn't put up with that incompetent behavior from a mechanic. If that younger mechanic understands how EGR systems work and fail he would be correct in suspecting the EGR valve. In this case, however, there are still enough of us around who remember the high failure rate of the distributor pickups and how they acted, ... So, ...

My recommendation is to request just the distributor pickup be replaced at this time. You can buy it from an auto parts store, then look at it to see if you want to replace it yourself. If no screws are rusted tight the job will take less than ten minutes. You can also request any mechanic replace it. Forget the EGR valve for now. You can always revisit that story in the future if there are still stalling problems or rough running at low engine speeds.

You're welcome. That brings up another point. In most dealerships, and many independent shops that have service writers, aka service advisers, those people often don't know much more about cars than the owners do. In every profession the professionals speak their own language. Part of the service adviser's job is to translate what the mechanic wrote on the repair order into something the customer can understand. Things can get lost in translation to the point the mechanic won't even recognize his own story when he hears it repeated by the customer. That is not an intent to defraud or mislead anyone but it can explain why you may get different stories from two different shops. We've all been to doctors who don't explain stuff very well and others who take the time to carefully answer every question. There aren't many mechanics who are good at explaining to customers what is wrong or what needs to be done. When you find one be sure to let him know you appreciate his efforts.

If it's running rough there is a misfire. That will slow the engine speed possibly to the point of stalling. Start with the normal tune-up items like spark plugs and wires.

If the battery was recently disconnected or run dead the Engine Computer lost its memory and has to relearn "minimum throttle" before it will know when it must be in control of idle speed. The engine will be hard to start unless you hold the gas pedal down 1/4". It also might not give you the normal "idle flare-up" to 1500 rpm when you start the engine, and the engine will want to stall when coming to stop. To meet the conditions for the relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the brake or gas pedals.