Can a POA be overturned, taken away or given to another family member?

If Grandfather is legally competent to make his own decisions, he could choose to move to a different facility than the one his 2nd wife chose...and his daughter is not forbidden from helping him look at different facilities. The 2nd wife might not like that but again, if the man himself is capable of saying he wants to live somewhere else, he retains that right to choose. If he is too far gone with Alzheimer's then the 2nd wife can do what she wants, but every one would hope that she take into consideration other close family members thoughts and concerns. If there are other facets (like maybe he's a vet and 2nd wife has him in VA home) sometimes that's a no-brainer.

If Grandfather is legally competent to make his own decisions he could appoint someone else to be his POA. But if he has cognitive issues to the extent that he can't explain what a POA is, he would probably not be eligible to do that.

The ideal situation here would be for step-grandma and daughter (and possibly granddaughter) to work together in grand-dad's best interest. Is that a possibility?

Even without a POA, a wife has first rights over a daughter. Give him time to settle in there. Taking him out only makes the patient more agitated. Having him at your home would mean you have to be there 24/7. Not a realistic option.