Does impurity transfer to me from my mother who does not cleanse herself after urinating and touches me immediately after leaving the restroom?

Not cleansing oneself after urinating is a serious matter and one of the causes of punishment in the grave, as the Prophet, peace and blessings be upon him, said: "They are being punished, and they are not being punished for a major sin [in their view], but indeed it is major. One of them did not shield himself from urine."

The mother should be advised gently and wisely if she does not cleanse herself.

Impurity does not transfer merely by touch; the original state is purity until impurity is established with certainty.