My mother has developed urinary and fecal incontinence. Has unresolved uti's and suffered a bad bout of constipation recently. Treatable conditions?

Very likely. That she can get some help for these problems - though realistic expectations are important. She should have a consultation with a urogynecologist. Someone who specializes in complex pelvic floor problems.
Probably. There is a need for more information. These conditions may be related. A bowel problem can cause UTI if there was a fistula (connection from the bowel to the bladder) for example. If that were so then a search can be made for the cause. It may be as simple as improving personal hygiene. She needs to see her doctor.