Your mother needs to see a doctor for a prescription remedy. Home remedies, over-the-counter products, natural stuff, heat, cold, whatever don't do much at all, although they may temporarily quiet the itch, depending on what you're using. I've tried just about every non-prescription option since my psoriasis appeared when I was nine years old, and believe me, nothing worked.
Plaque psoriasis (the most common kind, and what your mother seems to have) very commonly and stubbornly appears on the scalp, and can only be controlled (somewhat) rather than cured. There are many, many options your doctor can offer, and often the reduction of severity in breakouts is dramatic, although frequently not total.
I currently use a clobetasol preparation that is in mousse form - very easy to apply directly to my scalp, easily and quickly absorbed, quite effective. I put it on, let it sink in (and I can feel the lesions shrink after a few minutes), then go about my regular hair routine (after cleansing in the morning, and then on dry hair/scalp at night). It controls rather than cures, but it really helps the horrid itch and annoying flaking.
One reason mineral and other oils provide temporary or partial relief is that they can be used to loosen the scales that cover the red lesions underneath. Once the scales are moistened and gently rubbed off, topical meds can more easily reach the red lesions, where they can most effectively work.
However, removing the scales with oil and then not using a topical prescription med afterwards has only resulted in the return of the flakes/scales within the same day/night, because a hallmark of the autoimmune condition is extremely rapid skin cell turnover - the patches produce new, dead skin so fast that they build up almost immediately.
So, basically, go to a doctor. I spent decades on ineffective products before finally getting prescription stuff that markedly reduced my suffering.
2c, fine, extremely dense, color-treated, high porosity. Medium length (longest layer just grazes my shoulders).
mod-CG since 10/12