Certainly not here, where milk comes in bags. 
Is this 1960? Even people who mix milk from powder usually use plastic pitchers.
Why not just have a glass of milk she’s drinking? If she is also nursing the baby, in addition to using babyfood, she probably has a glass of something, because nursing makes you thirsty.
FWIW, though, the tiny spoons, and tiny bites you give a baby, are not conducive to your scenario.
It’s more likely she would miss a shard when cleaning, and the baby would pick it up and put it in its mouth. Babies put EVERYTHING in their mouths.
As far as whether she would be arrested, it really does depend on her background. Is she white? married? do all her children have the same father?
What you could do is put some other “suspicious,” but innocuous incident in her past. Maybe with a previous child, it fell out of its high chair, or off the couch, or the changing table-- most parents have a story like that. My son fell off the couch when he was ten months old. He could climb up and down off the couch, but just wasn’t very good at it. He had a pretty good goose egg on his head. We went to the emergency room. If he’d happened to have fallen at a slightly different angle and broken his nose, who knows whether that might have launched an investigation.
And FWIW, I actually did break my nose at the age of 13 months from falling out of my high chair.
Also, just a detail, when my son broke his arm at the age of 9 (from falling out of bed), someone came in to look at him, and made the note “normal bruising for his age,” which meant his shins had a couple of small bruises, but he had no large bruises on his back or face.
Anyway, that’s another thing-- if the mother noticed the baby swallowing something, and did something like try to smack him on the back, or Heimlich him to get him to spit it up, and he ended up with a large bruise, THAT would look extraordinarily suspicious to ER workers.
What** Alley Dweller **said. Jail or conviction is unlikely, but such a mother could very likely be vilified by the mobs on social media.
The “mother pouring from a glass pitcher right in front of a child” just doesn’t sound realistic in the 21st century. If I were reading this in a book, I’d think “Wait, why is it a glass pitcher? Is it going to break?” (That’s what I call the Plot-Driven Detail). When it did indeed shatter, I might stop reading the book at that point…
It doesn’t matter, people still use glass objects in their kitchen, something could shatter, far enough away from the child’s food that it wouldn’t seem to cause a problem, but a tiny shard of glass could travel far under some circumstance. The unlikelihood of such an event might arouse more suspicion by the authorities.
What, you people don’t have glass pitchers? It could be glass anything, people have glass. I think she could be arrested or not depending on how much trouble the writer wants to get her in and if she’s the protagonist, the more trouble the better.
Even more likely that it would be transferred to a kitchen serving container, rather than poured from the original packaging.
Short answer to the original Q, a court would use the reasonable-person doctrine, and determine whether there was neglect on the part of the mother to respond to what might have been a medical emergecy, At worst, negligent homicide.
Ask Dr Sears?
I’m envisioning a dude wearing Toughskin jeans who does Pap smears and colonoscopies using Craftsman tools.:eek:
ETA: if your insurance doesn’t cover the procedure, he refers you to old Doc KMart, the poorly shaven guy with the palsy and one milky eye whose white coat is yellowed with age.
On the results of swallowing glass shards:
Students hospitalised after eating glass shards in fried noodles meal
I’d say it’s highly unlikely anyone would be charged with a crime for this. (What specific crime/charge might you imagine?). Cutting to the chase, for the purposes of your story, you’re safe leaving it at that. As far as how the death occurs, however, you may want t to think it out more. Swallowing a glass shard might cause death in one of several ways: (1) The shard is swallowed, cuts some blood vessel as it passes through, and causes a large amount of bleeding. I’d say this is the least likely way. (2) As the shard passes through the GI tract, it cuts through the wall of the intestine, contents leak out into the abdominal cavity, the person gets peritonitis which leads to fatal sepsis. (3) The shard gets “misswallowed”, goes down the airway, and the person chokes. (4) The shard gets stuck in the intestine, causes obstruction, which then leads to a fatal complication. That’s about what I can think of. Other than the choking scenario, the death would be delayed from the swallowing. So to fit your narrative, as given in the OP, it would have to be the choking scenario. That would add an element of mystery/suspense, as in, no one would expect anyone to choke while eating puréed food. The whole thing seems pretty unlikely, which means it’s just the kind of thing a medical examiner (my job) might very well see.