He needs to file a motion for visitation. There will be a hearing and the judge will draw up an SPO, or standard posesion order. If he cannot document his time with the kids before it will be limited at first. So, he will need tor produce evidence that he has had time with the kids. It would also do him good to look at the laws regarding the recording of conversations in your state. If allowed he needs to do this. Nothing more powerful than going to court and you plop some tapes on the table...if mom has done some bad things and recorded it can be powerful...especially if she has lied under deposition.
Until he gets an order in place there is nothing he can do or anything to enforce.