A.T.
You might have heard that swallowed gum stays in your stomach for 7 years. That's not true. Though your stomach can't break down a piece of gum the same way it breaks down other food, your digestive system can move it along through normal intestinal activity. In other words, it will come out the other end when your daughter poops. Swallowing a large mass of gum, or many small pieces of gum over a short period of time, can block the digestive tract in rare cases. Blockage is likely when gum is swallowed along with foreign objects, like coins, or when swallowed with nondigestible materials like sunflower seeds even though this is not the case here.
There have been reports such as this one published as well.
SWALLOWING CHEWING GUM CAN BE HAZARDOUS TO CHILDREN'S HEALTH
August 1998 - Swallowing chewing gum can cause numerous health problems and it should not be given to young children who cannot understand this point, according to pediatricians from Nemours Children's Clinic, Orlando Fla., who compiled case studies to illustrate the potential health hazards of chewing gum for small children. According to the study's authors, swallowing gum can cause many adverse health effects, including diarrhea, abdominal pain, flatulence, mouth ulcers, and dental and jaw problems, and is not recommended for young children. In addition, it can block the esophagus and colon. The first case study highlighted in the study is that of a 4-year-old boy with a two-year history of constipation. After numerous tests and different treatments, doctors discovered that his fecal matter largely consisted of chewing gum. On further investigation they learned that the boy always swallowed his gum, after chewing up to seven pieces each day. In another case, a 4-year-old girl suffered from complications from constipation. Again tests and treatment failed until doctors removed a fecal mass of chewing gum. The child had the habit of swallowing gum, often just to get another piece. The third case concerned a 1-year-old girl who drooled, coughed and had trouble swallowing. Doctors discovered four coins encased in chewing gum lodged in her esophagus. The study's authors note that children who show signs of chronic constipation or acute coughing and drooling should be examined to determine whether chewing gum has been swallowed.
In either case, chewing gum is not a good choice, try jelly beans....same consistency yet those are meant for swallowing.
You don't even have to tell her it's not gum in the event a tantrum may follow. Good luck.