Would a mother be sinful if she did not inform her husband, who is an Imam, of their daughter's pregnancy out of wedlock and her giving birth, and concealed the matter?

The basic principle is to conceal the faults of a Muslim who is not known for committing sins. The mother does not incur sin by not informing the girl's father about her daughter's matter. If he comes to know, she should tell him that she did so to conceal the fault of a Muslim. She must also advise her daughter to repent to Allah for the sin.