The vet decided to put the ill dog to sleep. ( He decided to euthanize the dog)

It was almost midnight so I put my kids to sleep. ( He tucked them in, didn't kill them!)

The man found out his wife was cheating on him and put his wife and the kids to sleep ( He killed them)

From my understanding, put to sleep has two very different meanings. Am I right? Learners must be

very careful when using this phrase. Thanks in advance!
I'm not familiar with the usage in the third sentence. For me, putting an animal to sleep refers to euthanasia, and putting a human being to sleep is to be taken as putting them in bed.
I'd say it's very unnatural to apply the first meaning to humans, unless the author is trying to shock us with some kind of sick point. It's a euphamism for a socially acceptable but painful act. Murder isn't socially acceptable (in most societies.)
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New2grammarThe vet decided to put the ill dog to sleep.
Hi N2G
When ill means "sick", it should not be used to modify a noun: The vet decided to put the sick dog to sleep.
Funnily enough there is another phrase with the same double meaning

'to put down' (animals only) - to euthanase

'to put down' (babies) - to get them to sleep in their crib/cot/bed.

In normal useage, you don't ever use put down or put to sleep to mean kill humans. Perhaps if you were an author trying to make a point in a novel.
As you probably know, euthanasia for humans is a current topic of discussion among people involved in "medical ethics," and it's been practiced to some extent.
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Thank you everyone. I get it now!