Mother-of-two Clare Farley told ITV News she made the tough decision to have her cat put down when Jasper contracted tuberculosis as it was "terribly worrying".
Ms Farley told ITV News Correspondent Rupert Evelyn, "The fact that the younger [children] are their immune system is not built up yet ... I could not have a cat in the house that could potentially give them a really nasty disease".
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Two-year-old Casper Platt-May and his six-year-old brother Corey died in the crash in Coventry on Thursday.
It means the petition, calling for a diverse panel to be appointed to the inquiry, has enough signatures to spark a debate in Parliament.
American businesses have begun severing ties with controversial pro-gun group the NRA in the wake of the latest mass school shooting.