How do I get out of POA and health care proxy? There are two of us appointed and I am not the primary. My mom has dementia.

If you aren't the primary POA and health agent then you don't have to handle anything.
The only time you would have to be handling anything is if your mother's primary POA and health agent becomes unable to for some reason.

Step back and leave the primary to deal with matters. Explain you are not coping with it and need at least a break. Agree the length of time you need to be able to discuss things (probably at least 6 months) and sit down with the Primary at the end of the period and talk through the ways forward. I would not give up completely whilst you are not coping because you can always be taken off a POA but you cannot be added back on with mother having no capability to make the decision.
Not everyone is cut out to be POA by a long chalk, and if it turns out you can't then you have to discuss with the Primary if they can. You also need to agree between you whether you will have any input - if you do decide to step down then you will have no right to disagree with any decision they make even if you don't like it.

https://www.agingcare.com/questions/we-did-not-use-a-lawyer-we-did-this-on-our-own-im-sure-she-is-willing-to-do-this-considering-469008.htm

You have 2 postings going on the same subject.

I never had a Nurse involved with my POA. What can u be doing that is wrong? You pay her rent. Supply her with her toiletries and depends needed. My Moms AL handled her meds. Calling the Dr. Sending prescriptions to their pharmacy. She gets her meals. She is cared for by aides. What can u be doing wrong?

If there was a lawyer that you saw when POA was established contact them and say you wish to rescind your role as POA.
Have you talked to your sister about this? It might be possible that all you have to do is send notice to her as well as the facility where mom is living and inform them that you will no longer act as POA.
Side note here...You mention mom is in Assisted Living. At some point a move to Memory Care will probably have to be done. You might want to have some input in that.

You can officially resign but I don't know what the legal process is for that in your state and who you would need to inform. Does the other person have a grip on the management for your mom? Are they willing to continue solo? I would inform the other PoA in advance of resigning. If they get upset or freak out you can remind them that they, too, can resign.