When things like this happen, and sometimes the request for information is convincing and heart wrenching, I try to remember I'm not the school principal, I'm a representative of the Company with a duty to protect the Company's interests.  Generally, risk management trumps other types of concerns in a situation like this.  Generally, I can be counted on to tell people the company does not divulge information about its employees except when permitted by policy blah blah blah.

The minor might be emancipated.  The minor might be an adult, legally, even before 18, in your state.

The minor might have privacy rights (e.g., privacy regarding reproductive health information is not resolved in every state and there may be similar laws relating to employment information).

TXHRGuy gives you good advice.  I always stand by my policy not to give out information about an employee to anyone else without the employee's consent.  Since the employee doesn't want her mom to have the info then you shouldn't give it out.

I will never forget the day that the wife of one of my employees called me, demanding that I give her salary information for her husband.  She wanted his weekly pay, how much bonus he had received that year and also how much commission he received and what he was expected to receive for the rest of the year.  I calmly told her that I was unable to give her the information and that if her husband did not have the information, I could give it to him to bring home.  She got really mad and kept demanding that I give it to her.  I finally ended the conversation as politely as possible.  Then I went to go see him.  When I told him about the call, he said "you didn't give it to her, did you?"  He was really upset. I said no, that I don't ever give out that info without an employee's permission.  He was really happy.  Here is the reason why - I didn't know this but they were going through a really ugly divorce and she wanted this information to go after him.  He said she needed to get the information the correct way -through the attorneys.  Just goes to show that you never know why someone is asking for the information.

What kind of information was the mother looking for? I personally don't think you should be giving out any information. I have a 17 year old son. I called his work one day to see if he was working and they said that they could not give out that information. They wouldn't even tell me if he was there.

As a parent it was frustrating but as an HR person I understood their position. So I had to drive to the pizza place he was working at, could see him making pizzas and I was able to talk to him. 

She wants to know if her daughter put in for a leave request and if she did, did the leave get denied.  The mom is saying she’ll provide a letter from an attorney saying she is the girls legal guardian.

I definitely would stick to the policy of only discussing work related information with the employee.  I used to work HR in a retail environment and had parents call me to complain about scheduling of their son/daughter, time-off, pay, etc.  I just told them that I understood that they were concerned and if son/daughter wanted to discuss the issue, my door was always open.  Sounds like either the mother thinks the daughter was denied leave unfairly and wants to "fix it" or the daughter doesn't want to go to a boring family function (or something similar) and said she had to work and her leave was denied.  Either way, better to stay professional.  The daughter needs to learn to be responsible for bringing up her own issues at work if she thinks she was unfairly denied leave.  If not, she may be one of those kids bringing their parent to a job interview!

HRFLDist:

She wants to know if her daughter put in for a leave request and if she did, did the leave get denied.  The mom is saying she’ll provide a letter from an attorney saying she is the girls legal guardian.

As far as I know, mom is not entitled to that information, so there's no reason to disclose it to her.  There's probably a reason why the attorney is sending a letter saying mom is the legal guardian and not a letter saying mom is entitled to her daughter's work schedule information.

Edit: I know I wouldn't give that information to the spouse, either.  No reason to get in the middle of any of that.