Islam stresses the status of parents and the obligation to treat them with respect. Is it true that paradise lies under the feet of mothers and that if a mother is alive she can protect her children from God’s punishment with her daily and nightly supplications? It is said that this protection ends with a mother’s death. Kindly explain.

The statement that paradise lies under the feet of our mothers is figurative rather than literal. What it means is that a dutiful son or daughter is more likely to earn God's pleasure by virtue of their mother's continued supplications for them to be guided by God in everything that benefits them. Moreover, children become better individuals when they exert themselves to please their mother. They put their mother's happiness above their own which is the minimum reward a mother deserves after spending many years looking after them.

It is not correct to say that a mother’s supplications protect her children from God's punishment. If her children disobey God Almighty, nothing can protect them from His punishment; it is their good deeds that, with God's grace, can save them.

There is no doubt that dutifulness to parents is a good deed that is amply rewarded by God Almighty, but this is how far it goes. People normally exaggerate matters, and when they interpret figurative expressions literally, reach a false misunderstanding. To say that a mother’s supplications protect her children from God’s punishment as long as she is alive is one such false notion. [Added: It is understandable though, that a mother’s supplications for a dutiful son or daughter are more likely to be answered by God Almighty and thus protect them from evils. This should never be construed to mean that they can indulge in sin and hope their mother's supplications will protect them from God’s punishment.]
And God Almighty knows best.