It is not uncommon, actually its probably the norm, for parents to come up with all kinds of accusations - many petty - during a divorce.
Follow Stealths advice...or your dad should come on here to get advice...he needs to be actively getting in his car and going to pick up the kids on his court ordered time. If mom refuses to let the kids go...he needs to call the local police simply to have them write it up (not to get involved), so that there is documentation.
Has he been doing this? He can't just sit on the couch and say "I know she won't let me see them, so I'm not going" and then go to court and file for contempt. Next time he's in court, he should request makeup time.
He needs to ignore mom's accusations. It only puts the children in the middle. Here I am involving you...poor you...but this is a good example of how adults can get quite messy when splitting up/divorcing and there are kids involved. I learned my lesson the hard way...when you pick your man to have a child with, pick one that you know will always do the kind thing towards the family should it come to divorce. (not in the anticipation of a divorce, I have just found when I do that it knocks a few men off the radar)