A DUI will indeed show up in a criminal background check for 7 - 10 years from the conviction date.
There are no state laws that specifically prohibit you from working in day care, but the the day care company policy will dictate whether or not to use this as a screening method when interviewing for employment.
Keep in mind it is a misdemeanor, so when asked if you have ever been convicted of a misdemeanor, you have to say yes, because they will find out.
It is not the worst crime in the world, and some may not factor it in at all, some will. If asked about it, be honest, tell them you made a mistake. It will never happen again.
Should you require further clarification, please never hesitate to ask. It would be my pleasure to clarify issues related to your question.
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Regards,
Mike
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