I think it was a bit over the top considering it was her first offense and that his grandchild isn't at fault for her/his mother's narcissistic behaviour. I think he should have let her stay for the moment but warn her that if anything happens to the cat (even by "accident") he'll actually throw her out.
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So it is ok to put your child and innocent grandchild into a situation of homelessness without even checking if she is mentally ok? I mean, a pregnant woman who is single and has no place to live is certainly a vulnerable individual at a low point in life. If you, as family show no empathy then who should?