Does a mother's failure to pray affect her daughter, such that the daughter's supplications are rejected or she does not lead a happy life as a punishment for a sin she did not commit, but rather her mother did?

Prayer is a connection between the servant and his Lord, and a reason to avoid indecency and evil. Abandoning it severs this connection. Any deficiency in those who do not benefit from it stems from them, not from the prayer itself. Every Muslim must perform prayer without using the corruption of others as an excuse, for the Prophet, peace and blessings be upon him, said: "Do not be easily swayed, saying: 'If people are good, we will be good, and if they do wrong, we will do wrong.' Rather, accustom yourselves: if people are good, be good; and if they do wrong, do not be unjust." The mother's failure to pray does not affect her daughter, for Allah Almighty says: "And no bearer of burdens will bear the burden of another," and "Every soul, for what it has earned, is retained." The daughter should be good to her mother and strive to save her.