Barnes, whose mother is French and whose husband is Australian, has traveled to Australia and Canada with her children, and has generally been able to find foods her children can eat.
But not all of Barnes's travel experiences have been so positive.
She recalls a 12-hour flight she took to Sydney to visit her father-in-law in Queensland, Australia, when her oldest son was 3. The airline had a standard in-flight snack of peanuts, and made the family sign a waiver before they would allow Barnes and her family to board.
"Instead of trying to work with us, their reaction was, 'Well, that's the standard snack,'" said Barnes.
She spent the entire flight in her seat afraid to take her son anywhere else on the plane. But, she recalls, the flight staff was very accommodating, asking those around her family to have another snack instead of peanuts.
"The people at the gate and the people on the phone were the ones asking us to sign waivers," Barnes said.
Clowes recalls when she brought her son to an amusement park where she was told that one stand served nut- and dairy-free treats.
"The one place in the park that had a "safe" frozen treat also sold roasted peanuts — same clerk, same cash register. We couldn't risk it," she said.
Because of the unexpected problems, allergy doctors recommend plenty of preparation before traveling, including bringing your own food.
"The big thing when people [with allergies] travel is that they need to be prepared," said Sandra Gawchik, a doctor of osteopathy at Asthma and Allergy Associates in Upland, Pa. "You always have to call in advance for what you want."
Allergy doctors cite the need to eat out more when traveling — along with allergens from pets, chemicals and smoking in hotel rooms — among the biggest potential problems when traveling with allergies.
Gawchik made several recommendations when traveling by air, including flying first thing in the morning, when the planes have just been cleaned, and bringing wipes to clean the seat. Allergy patients should always have their adrenaline or epinephrine needles on them, with labels, along with a doctor's note to show to TSA.
Some parents of allergic children avoid flying altogether.
"We don't fly because we're fearful of even traces of peanuts on a plane," said Lenore Collins of Port Washington, N.Y., whose 5-year-old daughter's allergies include peanuts, dogs, cats and pollen.
In addition to driving to all destinations, Collins calls amusement parks in advance to ensure she can bring in food for her daughter, and even checks to the distance to the nearest hospital.
Clowes uses online maps to find supermarkets with allergen-free foods near their hotel. She also does a similar check to find area restaurants. Meanwhile, Collins won't even hazard a trip to a restaurant with her daughter, eating food entirely from supermarkets.
"I would never encourage anybody not to be as careful as they want to be," said Dr. Andy Nish, president of Allergy and Asthma Care Center in Gainesville, Ga. "If there is any question that you don't know what's in something, then it's best not to eat it."
But he feels that allergic travelers who want to eat out should take that opportunity.
"I wouldn't say you have to bring your own food to anywhere … There's a balance between being careless and being so concerned about it that it takes away all their fun," Nish said.
Many allergic travelers manage to strike that balance. Fisher said he has met a number of people in the travel industry with food allergies, including an editor who has many of the same he has. Despite these obstacles, Fisher and other allergy sufferers continue to travel the globe, sample the cuisine, and write about it. Food allergies haven't stopped their travel.
"If I were a purist," Fisher said, "I'd carry my own food wherever I went, I suppose. But I've been traveling this way for 49 years."
ABC News' Lara Salahi contributed to this story.