California doesn't have any state specific rules on deadlines to file a Motion in Limine. However, there may be local court rules that provide for such deadlines, or the judge may have signed a order regarding deadlines prior to trial for all motions to be submitted. So, it's impossible for me to say with certainty if you can still file.
As the previous expert noted, assuming you file the motion, approved or denied, chances are the father's lawyer is going to try and call the mediator as a witness, and if so, you'll want to object. If you filed the motion and it was granted, then you can simply argue that the mediator was excluded by the prior ruling, If you don't file the motion, or the motion is denied, you'll still want to make the same argument that you did make/plan to make in the motion in limine.
I think what the previous expert was saying about mediators testifying is that in some cases, yes, a mediator has been allowed to testify - in other words, it's up to the judge to decide.
Assuming the mediator is allowed to testify, you can question them on their report. Again, it's hard for me to tell you specifically what to do or so without knowing all the facts and reviewing documents (and even if I could do that, I cannot give you legal advice anyway), but it seems like from what I am reading, you should be able to get the mediator to admit that a) they are not an expert on child abuse
/neglect, b) they did not witness any first hand abuse or neglect of the child, and c) there are no substantiated reports of abuse or neglect of the child.