This is a very common saying and belief in every religion that sums up the importance of the mother as well as the obligation every child has towards their mother in order to attain paradise.
However, this does not mean that just by virtue of me being a mom, my jannah is pakki…The message is actually for the child to obey and respect their mother, therefore adding on lots of credits toward their ticket to jannah…but not for every mother to think that Oh now I’m a mother, I can do whatever, but I’m automatically always perfect.
yes, there is a Hadees but b4 anything else a person is to fulfill his islamic duties. if a person doesn't do salaat or haj or roza then he must not expect to go to jannat even if he treats his mother in the best possible way. one must fulfill his faraaiz alongwith Huqooq ul ibaad only then he/she can expect jannat and again without Allah's Mercy no one can enter jannat because we all do sins knowingly or unknowingly...Jannat is NOT our right, its a priviledge given by Allah.