Is a wife obliged to serve and care for her parents-in-law?

In terms of fiqh, caring for parents-in-law is not the wife's obligation, but being good to them is a noble trait that is strongly encouraged.
The duty of devotion to and support of parents in need lies on their child, that is, the husband. But parents-in-law are mahram and part of the wife's family; treating them well pleases the husband and strengthens family ties. The husband should not burden his wife with full-time care without her agreement or help. Care for the elderly is best shared with the husband's siblings. See Rights of husband & wife.