Welcome to HCM.
She must be having gastritis
or some other problem which is causing vomiting
The act of Vomiting produces increased intra-abdominal pressure, leading to release of anal sphincter, causing the stool to leak out.
At this age it is expected that a person will have poor control over bowel movement due to relaxed sphincter.
Her vomiting needs to be taken care of and the involuntary pooping will be controlled automatically.
Wishing your Mom. all the best.