AITA: Daycare Owner Charges $600 Late Pickup Fee

Over on Reddit you can find a bunch of posts of people asking if they are an A-hole for something they did. Here is a recent post about a daycare owner having to charge a mom $600 for being late.

I'm the owner of a daycare. Our entrance requirements are fairly lax compared to some others in the area, and because of this, we tend to accept children of lower income families or children with behavioral problems, etc. Not all of our children are like this, but the proportion of them is bigger than others.
We have a policy (which I'll say is very common with daycares) about late pickups. For us it's $3 per minute late. Some others in our city are $5, some are up to $10. The policy is in place because our employees, to be blunt, have places to be after work. Some have second jobs, some have to pick up their own kids, etc. If a parent is late to pick up, by law we need to have at least two caretakers here for even just one child. So this $3/min is to pay for the employees, the daycare sees none of it.
Last week, a mother was just over three hours late. We know she's of the aforementioned low income bracket family and we know she's a single mother, too. Her child is a darling, though. When we spoke about the late fee she got fairly upset and we reassured her it would be on her next billing cycle.
I wasn't on premises when this happen, but if I had been, I would have volunteered to stay late. This would drop it to $300, but I wasn't there. I can't stiff my employees or change the fee or waive a portion of it without dipping into my own pockets. I also can't ask my employees to be altruistic here because it's their money by rights (and the agreement I have with them). If she had even phoned in advance, I could have driven up to help out, but she didn't.
When December rolls around and she refuses to pay the money, she will be kicked out of the daycare. We don't know if she'll be accepted into a different one because of who we accept and our (cheaper) rates. She'll have to work juggling babysitters which I don't even know if she can afford.
I feel between a rock and a hard place whether I should extend a generous hand and just comp it. $600 is a lot of money and I already have the two employees asking about it, excited at the "bonus" they're receiving.
AITA?

After reading, there's still probably lots of questions. Well, the daycare owner answered some of those questions later on in the comment section.

Sorry I wasn't home to answer all the INFO requests, so here's some:
- mother's excuse
She didn't have one, other than she was sorry she was late. We asked if she was in an accident or something to that effect and she said no.
- employee salary
We offer $21.25/hr. Minimum wage here is $14.50/hr and the premium comes from the work environment and we incentivize hires. This is competitive for our area.
- why two employees
By law we need to have two caretakers for up to 12 kids, then 3 for up to 24, then 4 for up to 36, and so on. I imagine the justification is if one is incapacitated, one is still there.
- emergency contacts, etc
All of her contacts stated she was on her way. We would normally call emergency services in times like this but it's left to the employee to gauge the situation. We've never had to call before: if an emergency contact says she's on her way, we take it at face value.
- who gets the money
I see not one penny of it. The late fee is paid directly to the employees.
- conflict of interest
We have parents sign in when they drop off and sign out when they pick up. We use a tablet for this, so it's not a matter of employees erasing or striking out a name and cashing it. They have no control over the program.
- why wait
My employees tried phoning the mother and her phone was off. This is at 30 minutes. Then at 60 minutes they refer to emergency contacts. We've never had to call CPS or 911 before, and I try not to let that happen. We don't want to call CPS and then a minute later they show up: this is more trouble than the late fee is, anyways. The emergency contacts, four of them, told us they were in touch with her and she was on their way.
- the $3/min fee
I think it's reasonable. Two of my four employees have children of their own in childcare with similar late policies. One of them has a night shift at another job. This fee is there to protect my employees and our patrons: I can't have an employee leave before everyone is picked up, that's unsafe. The $3/min is to ensure if they themselves incur costs due to them being late to whatever, that they're compensated.
Everything else is clearly stated in the OP. If I see other unanswered INFOs, I'll edit this.