When you cook with something like red wine in an Italian sauce for example, you're not using all that much, so even if the alcohol isn't burned off fully, you're really not going to be ingesting very much. 1/4 cup of red wine in a massive bowl of spaghetti sauce won't give you very much alcohol once placed on the plate.

I always thought it burned off totally myself, but when I looked up information about that I found websites saying that quite a lot of it is left behind, so I don't really know what is real.

I personally wouldn't worry about it too much. Just my thoughts.

btw, you can buy something called verjuice or verjus. It's made from unfermented grapes and is alcohol free. Used for cooking purposes. Maybe if you're concerned you could buy your mum a bottle of that for the kitchen.