“Is a “Limited Power of Attorney” useful for child care issues, i.e. temporary guardianship, school related issues, child care, child support, etc.?”
This is a broad category of issues and situations listed here, some of which may be addressed by limited power of attorney, and some of which may not be. The question is also very broad. So, in short, the answer is “it depends”. Whatever it is that you are trying to accomplish here, it sounds as if you should consult with a family law attorney. Such consultations are usually free.