I feel that folks without a gall bladder definitely need to flush the liver, as the gall bladder acts as storage for the bile the liver produces (up to a quart and a half daily). When there's no place for it to be stored, the liver has to make more than usual (as I understand it).
Flushing the liver is safe for those without gall bladders.
I'm sure that a series of flushes will be extremely beneficial to your mother's health & well being.