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He has the right to petition the courts for custody of the child for neglect on your part. He would have to prove that the older child is not caring for his child properly. There are state laws that require children to be emotional capable of watching a younger child. Not all states have these laws but even those who do not most often would not agree with a 11 year old babysitting a 7 year old. Typically 13 is the accepted age to babysit.....though in the end it will be up to the judge.
I would advise you in the meantime to not allow the 11 year old to abbysit any longer to prevent a problem in the courts.