Is caring for one's elderly mother-in-law at home, even though her children are well-off, considered part of honoring one's parents, and will one be rewarded for it like the reward for honoring one's parents?

There is no doubt that one earns reward for being kind to his wife's mother if the intention is sincere, for Allah Almighty says: "Indeed, Allah loves the doers of good." As for whether the reward for this kindness reaches the level of honoring one's own parents, this is part of the unseen, and it is hoped from Allah that the doer of good will attain a similar reward.