If one child is the caregiver and the other does nothing do they have to compensate the caregiver?

No one owes anyone else anything, to my knowledge, unless you have a written, legally enforceable contract.

my wifes father has early stage alzheimers her mother has stage 2 alzheimers. we had to give up our home and move in with them.her father also has muitiple colapsed disk in his back and is unable to do much.she can not take care of them by her self.i may have to leave my job to help her.we are not putting them in a nursing home.is there any assistance ou t there that would pay me and my wife to care for her parents.

As far as I know siblings are not obligated by law to pay another sibling to provide care. There are programs out there to assist in providing in home care for elderly/disabled living in the community. For example, there is the Elderly Case Management Waiver that pays a case manager of your choice to assist the family with coordination of services. There is also the Elderly and Disabled with Consumer Direction that pays to have a facilitator come to the home and trains the family/individual/caregiver to be an employer and hire staff that can provide person care, supervision, and other services. The individual needs to meet the Level of Care Criteria (essentially nursing home level of care) and the financial eligibility requirements. Your local DSS and Health Department can be contacted to request a screening for services.