The VA won't seek reimbursement from your father's estate for VA-sponsored nursing home care. Whether the state seeks reimbursement is more complicated.
If your father lives in a private or state-run nursing facility, rather than in one actually operated by the VA, there may be costs in addition to what the VA pays. If so, your father might qualify for Medicaid (Medi-Cal in California) to pay those extra costs. He might be eligible for this Medicaid nursing home coverage even if your parents own a home and your mother still lives there, and your parents have some other assets and income. However, if Medicaid does pay for some of the nursing home bills that the VA doesn't pay, after your father's death the state could seek reimbursement from your father's estate. (For a discussion of Medicaid rules having to do with nursing facility care, take a look at our article Will Medicaid or Medicare help pay for my mother's long-term care?.)