K.P.
UPDATED:
Again, I respect your point, but you are assuming that she's unsafe while she's there, which may or may not be the case. Don't go through him to visit the daycare- you don't have to. Call them yourself, explain the situation and schedule a tour. If they don't allow you to visit, then you have reason to be angry and suspicious of them. Reputable facilities have a "welcoming" policy and will be happy to give you the chance to see the space. When you are there, come prepared with the custody documents and ask that your name be listed- while you are standing there. I have done this numerous times when I was an assistant principal. Believe me, no facility wants to get in the middle of a nasty custody battle. They are an administrative nightmare and are rarely about the child.
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What is your issue? Is it a licensed daycare? What makes you think that she's there illegally? If he's a custodial parent, he can enroll her in daycare and have her there during "his time" if that is what he wants to do.
If you show up at the daycare center and try to pick her up without his written permission, the daycare center will not allow you to take her and why would you do this?
This sounds more like an issue of jealousy on your part & is NOT an issue for Social Services. She's not being neglected or abused. If he has to work, he has to work... it's still "his time" with her. You have no idea whether or not the enrollment information is correct and you are making the assumption that b/c her stepmother works there, she's just "hanging out" without paperwork.
From your previous posts it seems like you really don't have the resources to be suing him over something that isn't illegal. Many daycares allow employees' children to attend without charge as "back up" care. You would have caused a horrendous scene and possibly gotten the wife fired b/c of your immaturity and jealousy.
He's her father, he has joint custody and he's working. If he needs child care during that time, then he has the right to enroll her. He does not need to have you as a babysitter. You have nothing to gain her, but a lot of $$$ to lose, especially if the facility files a restraining order against you to keep you off of their property.
Now, if you would like to tour the facility then do so with honesty and some dignity. Call the place, calmly and maturely explain the situation and simply ask if you could take a tour. They will likely call your ex to verify the story, but will also likely invite you to come and see the place.