My husband's children want to know what happens if I die how do they become POA?

You can appoint them as seconds on your POA.

Check your POA, does it authorize you to appoint a successor or a CO-POA?
If not the children will need to go to court and have themselves appointed as Guardians. This is the result of failure to complete the advance planning

First, did he want them to have that role when you designated you with the powers?

Second, if he did, the DPOA and/or Living Will should have designated them as successors, to act only upon the event of your death or resignation of responsibilities.

I have medical and legal authority under my father's Trust to designate successors if I'm incapacitated or unwilling to serve. Successors are also named if I die before the Trust is closed.

Third, at what stage of Alzheimer's is he? Was he admitted to the nursing home with signed medical diagnoses of Alzheimers?

If he's still competent to make decisions, AND if he wants them to be successors, he should have the attorney who prepared the documentation prepare another (or amend the first) to include them.

If he doesn't want them to play that role, they should be told, preferably by him. Alternately, you can just let the issue drop as they may very well become annoyed with you if they really want the powers.

If he's not competent to make decisions, and if you agree that the first marriage children should be successors, you'll have to have an attorney make the changes. This is not a DIY matter.

I think the additional issue would be who is named as Personal Representative (Executor/Executrix) of his Will?

...so sorry; hands do stuff. As I was saying, purchase a legal package from a stationary store or see an attorney. I had done this myself when my husband was first diagnosed. If there is a lot of $ here, see to it now. If it is a last ditch attempt to help dad, reach out to them.
Depending on what state where you live, will determine a lot. Check it out. Call ,"Elder Care " in your area. There are many social services to help you.
Enviable-we all die alone ,we all die, it's all stuff. $=funny pieces of paper with funny looking men on them????? Where do you put your worth? This is what I ask myself. Moment by moment...Seem to always get the same answer...You Are the Blessing.....

You are the acting POA. Upon death, the POA is not worth anything. You cN ALWAYS PURCHASE A LEGAL PACKAGE WITH Q

Time to consult your Attorney who wrote up the POA.

If he is still considered competent, your husband can change the POA to make you the primary POA with one or more of his children to be secondary who would become primary if you were to die. However, if he is no longer considered competent, one of them will need to file for guardianship if you were to die.