Is my mother required to make up the missed prayers that she left for 14 days due to a psychological illness that caused her confusion in prostration and bowing and sleep during prayer, knowing that she is now in good health?

A person afflicted with a mental illness falls into two categories:

The first case: If the illness leads to a cognitive impairment that prevents discernment, then prayer is not obligatory for them. They are relieved of accountability, like an insane person, a mentally deficient person, or someone who is asleep. This includes dementia. If the mother has suffered cognitive impairment due to mental illness, she is not obligated to make up the prayers she missed.

The second case: If the illness does not reach the point of cognitive impairment, and is limited to depression or distress, then they are accountable and all acts of worship are obligatory for them, just like a healthy person. If they experience periods of insanity interspersed with periods of lucidity, then they must pray during their periods of lucidity and make up what they missed during the times their intellect was absent.