I really do not think there is a legal age or time limit, it probably depends on the situation. You could go back to court and seek an order that if one parent can not be with the children for over 1/2 an hour the other should be given the option to babysit (depends on how close you live to each other)
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There is not a law governing the age of babysitters. Generally, babysitters are chosen by families according to age, maturity and ability to handle emergencies. It is a matter of common sense. Since you and your husband are uncomfortable with having the 12 year old placed in the position of "babysitter," I would simply suggest speaking with their mother about your concerns and that you would be more than willing to babysit when she goes to work or needs to leave the kids alone for any period of time over 1/2 hour. A responsible babysitter is necessary if you don't trust that either the 12 year old or 10 year old would know what to do if an emergency situation occurred. Kids fall down and break bones, cut their fingers with scissors and eat things they're not supposed to eat; and if they aren't prepared to deal with the consequences, then a babysitter is a necessity. Good luck to you.
The opinions and answers provided by Matthew Langhals, Attorney at Law do not constitute legal advice. If you are seeking legal advice, it is highly recommended that you retain an attorney and provide the details of your legal issue so he/she can advise you competently and properly.