This happened to us on vacation in Italy 2 weeks ago, my almost 2 years old daughter was drinking water from glass wine (since some better restaurants there don't give you any other type of glass regardless of drink).

We obviously freaked out and acted immediately, the staff was a bit concerned but it wasn't their child chewing glass shards. Daughter fortunately developed quite a skill or pushing stuff she doesn't like from her mouth using tongue, so she pushed out everything quickly, small cut in her inner mouth, 2 minutes of crying, us running around and that was it, with some evening worries (wife is a doctor but still...).

Not recommending this experience, better check what they give to your young ones (say below age of 3) beforehand, or just bring your own unbreakable one, even if (good) plastic.