There is something called Porcelain glue but I think that is to glue broken bits together, and I assume you don't have the bit that chipped off.
So you need to fill the hole.
Loctite make a gel superglue. You might be able to fill the chip with that and then smooth it gently with an emery board.
My glue of choice is always Araldite - it is an epoxy resin and comes in two tubes that you mix together before you apply.
when mixed it is quite stiff so it might fill the hole, then when it dries you should be able to gently sand it down with an emery board or a fine sandpaper.
I get a bit of tinfoil [the little tin thing a tealight come in is perfect] - I quirt a bit of each tube onto the foil and mix together with the end of a matchstick. I use the matchstick to apply the glue. It also comes with a little spatula, so that might help you apply it smoothly.
Obvs just hand rinse the mug in future and avoid the dishwasher.
Also I bet theres some youtube videos giving advice on how to do it.
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Further thoughts............
google your local area, is there someone who makes mugs - actually makes them, not buys blank white ones then adds a picture - an actual ceramics artist???? Maybe they have repair skills????
Alternatively, here is an attempt at copying the image on the broken mug.
You can have it put onto a new blank mug. I know its not THE mug your mum gave you, but maybe having a similar picture on a new mug will still give comfort???
I won't be offended if this suggestion is a big no-no, but here it is anyway....
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and a cropped version..
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