You say you have sole physical, but what about legal? If you have both, then as long as you can show you're taking the necessary steps, I think you're okay. However, if he has joint legal then he can petition the courts to investigate this on his behalf (and should he be wanting a custody change, it MAY look bad - not for certain, but you know how that goes).
However, that's a separate issue from CPS - he's a dope if he thinks he can call up CPS and tell them the truth of it all and expect them do run over to your house. As a teacher and a mandated reporter, it takes a helluva lot more than that to get them on your doorstep. The fact of the matter is, CPS doesn't want to take kids unless absolutely necessary. I've worked with CPS in two different states, and each time they've been calm, helpful and understanding - not irrational door-busters out to steal your kids in the night.
Back to the matter of what type of custody you share. If it is joint legal, then if push comes to shove (and your ex wants to fight it in the courts) you do have to take his concerns into consideration and come to an agreement about what needs to happen. However, if he has no legal recourse, while it would be nice to be able to work together, you have the final say. Then, be confident in what you're doing, and if you are certain you are taking all the steps you need to be taking to get your daughter her rightful education, you can tell your ex to piss off.
GL!