What is the ruling regarding the prayer of my mother, who experiences involuntary urination, has a scattered mind, and does not pray, despite having performed Hajj and Umrah?

Prayer is not waived for a Muslim as long as they possess their intellect. If illness has overwhelmed your mother and she has lost her mind, then prayer is not obligatory for her, as her accountability has been lifted. This is based on the Prophet Muhammad's (peace be upon him) saying: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches maturity, and from the insane person until he regains his sanity." However, if she sometimes regains consciousness and sometimes loses it, then prayer becomes obligatory for her if her period of lucidity coincides with its time. She must make up any prayers she missed if she regained consciousness and did not pray. Her involuntary urination falls under the ruling of سلس ( سلس البول - urinary incontinence). She should pray sitting if she is unable to stand, and lying down if that becomes impossible.