(A little background about where I get my info from: I have worked on food counters,
butchers and fishmongers, as well as in a restaurant with my boyfriend, so we've both done heaps of training vids and stuff

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My Advice:
People who get ill on holiday usually attribute it to food poisoning from "restaurant X" or "hotel Y", but it is actually often quite hard to directly pin point a location or a source, because of the range of activities that people partake in. Usually, a restaurant will be blamed by people without the proof of a pathogen or bacterial test.
Similarly, if a group of people at the same hotel fall ill, then the hotel is blamed. However, say the group of people "eat out" at a different place every lunch and dinner for a week, then that is 14 different places they could fall ill from.
Whilst the chances of one of them falling seriously ill from one of the meals is pretty low, the chance of a tummy bug increases if factors such as salad and ice cubes that come into contact with local water occur. This can happen at a plethora of locations so accusing just one place is a bit silly.
A main cause of sickness is "cross contamination", where a chef will cross from a raw to cooked food product without washing hands or utensils. If you can, take a sneak peek into the kitchens. My usual judge of cleanliness is "does it look cleaner than my local takeaway?"... It may sound silly but it works for me. If the country you are visiting has a food safety certificate scheme or restaurants then don't be afraid to ask to see a copy- an "A" grade can mean a happier and healthier holiday than an "E"
I'd say mummy is right in this case. I'd just advise you to trust your "gut instinct" with regards to food, and don't feel obliged to eat just to be polite or not to offend, don't worry about sending food back or querying it's preperation. If a bartender gives you a drink with ice in, and can't satisfy you that it is made with bottled water, ask for a new drink (watch so that they don't just take the ice out!)- they should be happy to oblige.
If there is any local dish you'd like to try, but you are not sure if you would be able to tell whether it is cooked properly or not due to an unusual foodstuff, then read up and learn about how it should taste, smell and it's texture and colour. For extra peace of mind, use websites such as holiday forums to ask for reputable places to eat, or about the catering facilities in your own hotel. That way you can make an educated guess about your health.
If all else fails though, getting ill is not the end of the world- usually a pack of immodium will see you through! Remember, one persons food poisoning is another persons hangover!
I have been abroad loads of times as a kid, and I've only been ill once, despite having a pretty adventurous family who would tend to eat out rather than in the hotel.
Don't be afraid to try anything new! After all, new experiences is why most of us go abroad... (apart from the cheap sangria, sun, sand and "the other one"

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Hope you have a good holiday
Marianne