W..
When you take legal actions you do so for basically 3 reasons. To recoup losses you've incurred, instigate a change in behavior or environment or to punish the daycare.
Recouping losses.
If you have had to pay above and beyond your insurance then the day care might be accountable for payment of those bills. So, your co pay and band-aids, neosporin etc and maybe lost time from work. You're talking about under $500, I would assume. It will cost you more to hire a lawyer than that. So, you wouldn't actually be gaining anything. The judge might even see this a frivolous lawsuit and order you to pay the legal fees of the daycare.
Change of Behavior / Environment
In this case, if your daughter is the first person to fall and they immediately added wood chips to the pile as you requested then you've already accomplished your goal without you having to pay for lawyers and have a long drawn out court case.
Punitive Damages
If the daycare was "willfully negligent" by not having the gap filled with wood chips (which means that 12 competent adults would have to rule that if they saw the step it would have to register with them that it might be dangerous BEFORE an accident occurred). Would 12 competent adults be able to find that the daycare knew it was dangerous and did nothing, risking the safety of their kids? Had you ever been on the playground and walked down those steps? if it's cement that extends from the last step to where the playground starts and there is a natural divider between the two it's hard to tell without seeing a picture. But if they didn't know it was unsafe and did nothing, willfully.... then you have no lawsuit.
Also as far as punitive damages, I'm not sure the scar of one toddler will inspire a judge to award you a large settlement of money. If your daughter were disfigured, that's another issue. A scar from her hairline to her eyebrow when she's a toddler will only be "damaging" to her if YOU let it be and if you teach her to focus on the scar.
Now that they have filled the gap with wood chips, have you kept your daughter there? That means you feel that she is safe enough in their care after they fixed the issue that led to an ACCIDENT.
I know it is frustrating when our baby gets hurt. But unless you plan on wrapping her in bubble wrap and storing her in a closet she will get hurt again. and again. and again.
I haven't seen the scar, but to say 'nothing will ever make up for the fact that my 2 year old has a scar" tells me it's either a really disfiguring scar or you are being a mamabear. If you're being a mamabear, that's understandable but we can't punish everything and everyone that hurts our kids.
"Doing right by your daughter" means teaching her the spirit of forgiveness and moving on and that accidents happen.
Good Luck.