Does having a general durable POA give me the right to take away car keys?

Read your POA to understand when it takes effect. It might require a doctor's note. If your DPOA is active and allows you to do so, you should sell her car. Out of sight, out of mind. Your conscience should tell you that you don't give her keys back. If she killed herself or someone else, how could you live with yourself? If the keys are what she's obsessed with, then give them back but disable the car by removing the spark plug wires. (The battery is too easy to fix.)

Since she's a runner, she'd likely be safer in a memory care facility.

The technical term for what mom is doing is "elopement" and it means she needs to be in a secure facility.

Sell the car.

I hope that your DPOA is now activated completely, and if not it should be with the appropriate doctor's letters.

I hope you are in charge of your now diagnosed mom, and are keeping her safe with 24/7 care as that is your Fiduciary Responsibity under the law.

If placement is necessary for your mother you will soon enough recognize that.

Of course there is no question of her now using the car. It should be removed, and sold with your DPOA. Your mom's license should be surrendered to the DMV and an identity card made instead.

I was POA for my brother. He was diagnosed with probable early Lewy's Dementia. He made me his POA and Trustee. One of the FIRST THINGS we did was get rid of his truck (already having been in one accident), surrendered his license, changed his accounts for his protection giving him a small spending account. As well as this I created his files, paid his bills, and we chose a good ALF for him.

This is your duty. You are not allowed to shrug now and let your mother run away, let her drive away, or let her be otherwise unsafe for herself and others. If you are uncertain of what your duties are now please see an elder law attorney. Your mom's money pays for this.

If her doctor says no more driving then he needs to report her to DMV or at least give you a letter u can take to DMV with you and have her licence revoked.

DPOA really does not give u that right, its a financial tool. But, as her child, you do have a right. She no longer can make informed decisions. You need to protect her and others. Stick to ur guns.

as others said, don't give the keys back. she could kill someone on the road. OP, you wouldn't be responsible for any driving accident. but morally-speaking, it's the right thing to do, to take away the keys, just like you would never give a drunk person a loaded gun.

i just want to point out:
"I hope you are in charge of your now diagnosed mom, and are keeping her safe with 24/7 care as that is your Fiduciary Responsibility under the law."

that's incorrect.
POA does not give you any legal obligations --- the decisions you take, should be in her best interests. but you're not under any legal obligation to take any decision. POA gives you the - possibility - to take action. it's doesn't oblige you to take action. the morally-correct thing to do, if one has no intention to help, is to resign from POA.

but POA doesn't in any way give you more obligations to help, than any other person, like let's say some other family member.

under extreme circumstances, only sometimes, adult children can be held responsible for abandoning or neglecting their elderly parent. but that has nothing to do with whether you're POA or not.

I would not give her the keys back under any circumstances.

I would let her stay at her friends, call her bluff, she will return home,

I would start looking at MC facilities to place her, she needs to be on lock down.

She needs more help than you can provide to her, time to rethink this entire situation.
Good Luck!

How about moral responsibilty? It is time to put her in a more secure environment as she will eventually hurt herself and me.

You should be "blaming" the fact of taking her keys away on her doctor, since they are the ones who said she shouldn't be driving. And they are correct, she SHOULDN'T be driving.
DO NOT under any circumstances giver her the keys back, unless of course you've disabled the car first. It's certainly not fair to unsuspecting drivers to have to risk being hurt or killed by a demented woman now is it? And yes, she would be held liable if something bad happened while she was driving and could lose everything in a lawsuit, and perhaps if she's living with you and you knowingly let her continue to drive(against doctors orders), and she injures or kills someone, you could be held liable as well.
So please continue to use your common sense and do whatever you must do to keep your mom safe, including placing her in the appropriate facility.

Let’s make lemonade.

She is out of the house. Good. Find her a memory care and move her from friend to memory care.

Assuming here you have all the necessary authorization to act.

She needs to be in a locked facility NOW.

Don't give her the keys. She is a safety risk to herself and others. You don't want to be dealing with the legal issues that could result from your knowing she's a safety risk and giving her back her keys. Yes, you could be held liable for accidents she causes. And no, you don't want to be looking down at her dead in her coffin after she kills herself and others by driving her vehicle when she shouldn't have.

She hates you and never wants to see you again, but she'll forget about that. She has dementia.

I don't know why she moved in with your friend or how the friend contributes to mom's eloping, but this isn't a good place for the friend to be either. You both have quite a problem on your hands, but you can solve it by getting mom into memory care, whatever it takes.